So here we are, testing both:

ppa:x2go/stable repo removal
ppa:x2go/saimaa repo add

The removal part, first:

##################
root@noc /var/log/apt # sudo apt-add-repository -r ppa:x2go/stable
Quick howto to turn your machine into an X2Go server:

sudo apt-add-repository ppa:x2go/stable
sudo apt-get update
sudo apt-get install x2goserver x2goserver-xsession
sudo apt-get install x2gomatebindings # if you use MATE/mubuntu
sudo apt-get install x2golxdebindings # if you use LXDE/lubuntu

Quick howto to install the x2goclient:

sudo apt-add-repository ppa:x2go/stable
sudo apt-get update
sudo apt-get install x2goclient

Enjoy!
More info: https://launchpad.net/~x2go/+archive/ubuntu/stable
Press [ENTER] to continue or Ctrl-c to cancel removing it.
root@noc /var/log/apt #
##################

Now the second part:

##################
root@noc /var/log/apt # sudo add-apt-repository ppa:x2go/saimaa
Bundle release of X2Go named ,,Saimaa'' (based on X2Go Server / Client 4 / nx-libs 3.5.0)
More info: https://launchpad.net/~x2go/+archive/ubuntu/saimaa
Press [ENTER] to continue or Ctrl-c to cancel adding it.

Hit:1 http://mirror.hetzner.de/ubuntu/packages focal InRelease
Get:2 http://mirror.hetzner.de/ubuntu/packages focal-updates InRelease [114 kB]
Get:3 http://mirror.hetzner.de/ubuntu/packages focal-backports InRelease [108 kB]
Get:4 http://mirror.hetzner.de/ubuntu/packages focal-security InRelease [114 kB]
Hit:5 http://de.archive.ubuntu.com/ubuntu focal InRelease
Hit:6 http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu focal InRelease
Ign:7 http://linux.dropbox.com/ubuntu disco InRelease
Hit:8 http://linux.dropbox.com/ubuntu disco Release
Get:9 http://de.archive.ubuntu.com/ubuntu focal-updates InRelease [114 kB]
Ign:10 http://ppa.launchpad.net/x2go/saimaa/ubuntu focal InRelease
Get:11 http://de.archive.ubuntu.com/ubuntu focal-backports InRelease [108 kB]
Err:12 http://ppa.launchpad.net/x2go/saimaa/ubuntu focal Release
404 Not Found [IP: 2620:2d:4000:1::3e 80]
Get:13 http://mirror.hetzner.de/ubuntu/packages focal-updates/main i386 Packages [836 kB]
Get:14 http://mirror.hetzner.de/ubuntu/packages focal-updates/main amd64 Packages [2,611 kB]
Get:15 http://security.ubuntu.com/ubuntu focal-security InRelease [114 kB]
Get:16 http://mirror.hetzner.de/ubuntu/packages focal-updates/main Translation-en [439 kB]
Get:17 http://mirror.hetzner.de/ubuntu/packages focal-updates/main amd64 DEP-11 Metadata [274 kB]
Get:18 http://mirror.hetzner.de/ubuntu/packages focal-updates/restricted amd64 Packages [1,937 kB]
Get:19 http://mirror.hetzner.de/ubuntu/packages focal-updates/restricted Translation-en [273 kB]
Get:20 http://mirror.hetzner.de/ubuntu/packages focal-updates/universe i386 Packages [730 kB]
Get:21 http://mirror.hetzner.de/ubuntu/packages focal-updates/universe amd64 Packages [1,067 kB]
Get:22 http://mirror.hetzner.de/ubuntu/packages focal-updates/universe amd64 DEP-11 Metadata [410 kB]
Get:23 http://mirror.hetzner.de/ubuntu/packages focal-updates/multiverse amd64 DEP-11 Metadata [940 B]
Get:24 http://mirror.hetzner.de/ubuntu/packages focal-backports/main amd64 DEP-11 Metadata [7,952 B]
Get:25 http://mirror.hetzner.de/ubuntu/packages focal-backports/universe amd64 DEP-11 Metadata [30.5 kB]
Get:26 http://mirror.hetzner.de/ubuntu/packages focal-security/main amd64 Packages [2,209 kB]
Get:27 http://mirror.hetzner.de/ubuntu/packages focal-security/main i386 Packages [602 kB]
Get:28 http://mirror.hetzner.de/ubuntu/packages focal-security/main Translation-en [356 kB]
Get:29 http://mirror.hetzner.de/ubuntu/packages focal-security/main amd64 DEP-11 Metadata [59.8 kB]
Get:30 http://mirror.hetzner.de/ubuntu/packages focal-security/restricted amd64 Packages [1,802 kB]
Get:31 http://mirror.hetzner.de/ubuntu/packages focal-security/restricted Translation-en [253 kB]
Get:32 http://mirror.hetzner.de/ubuntu/packages focal-security/universe i386 Packages [600 kB]
Get:33 http://mirror.hetzner.de/ubuntu/packages focal-security/universe amd64 Packages [842 kB]
Get:34 http://mirror.hetzner.de/ubuntu/packages focal-security/universe Translation-en [173 kB]
Get:35 http://mirror.hetzner.de/ubuntu/packages focal-security/universe amd64 DEP-11 Metadata [95.4 kB]
Get:36 http://mirror.hetzner.de/ubuntu/packages focal-security/multiverse amd64 DEP-11 Metadata [940 B]
Get:37 https://esm.ubuntu.com/infra/ubuntu focal-infra-security InRelease [7,453 B]
Get:39 https://esm.ubuntu.com/infra/ubuntu focal-infra-updates InRelease [7,452 B]
Get:40 http://de.archive.ubuntu.com/ubuntu focal-updates/main amd64 Packages [2,611 kB]
Hit:41 http://download.virtualbox.org/virtualbox/debian hirsute InRelease
Get:42 http://de.archive.ubuntu.com/ubuntu focal-updates/main i386 Packages [836 kB]
Get:43 http://de.archive.ubuntu.com/ubuntu focal-updates/main Translation-en [439 kB]
Get:44 http://de.archive.ubuntu.com/ubuntu focal-updates/main amd64 DEP-11 Metadata [274 kB]
Get:45 http://de.archive.ubuntu.com/ubuntu focal-updates/restricted amd64 Packages [1,937 kB]
Get:46 http://de.archive.ubuntu.com/ubuntu focal-updates/restricted Translation-en [273 kB]
Get:47 http://de.archive.ubuntu.com/ubuntu focal-updates/universe amd64 Packages [1,067 kB]
Get:48 http://de.archive.ubuntu.com/ubuntu focal-updates/universe i386 Packages [730 kB]
Get:49 http://de.archive.ubuntu.com/ubuntu focal-updates/universe amd64 DEP-11 Metadata [410 kB]
Get:50 http://de.archive.ubuntu.com/ubuntu focal-updates/multiverse amd64 DEP-11 Metadata [944 B]
Get:51 http://de.archive.ubuntu.com/ubuntu focal-backports/main amd64 DEP-11 Metadata [7,976 B]
Get:52 http://de.archive.ubuntu.com/ubuntu focal-backports/universe amd64 DEP-11 Metadata [30.5 kB]
Get:53 http://security.ubuntu.com/ubuntu focal-security/main amd64 DEP-11 Metadata [59.8 kB]
Get:54 http://security.ubuntu.com/ubuntu focal-security/universe amd64 DEP-11 Metadata [95.4 kB]
Get:55 http://security.ubuntu.com/ubuntu focal-security/multiverse amd64 DEP-11 Metadata [940 B]
Reading package lists... Done
E: The repository 'http://ppa.launchpad.net/x2go/saimaa/ubuntu focal Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
N: Skipping acquire of configured file 'non-free/binary-i386/Packages' as repository 'http://download.virtualbox.org/virtualbox/debian hirsute InRelease' doesn't support architecture 'i386'
N: Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository 'http://download.virtualbox.org/virtualbox/debian hirsute InRelease' doesn't support architecture 'i386'
root@noc /var/log/apt #
##################

The "sudo apt update" part:

##################
root@noc /var/log/apt # sudo apt update
Hit:1 http://mirror.hetzner.de/ubuntu/packages focal InRelease
Hit:2 http://mirror.hetzner.de/ubuntu/packages focal-updates InRelease
Hit:3 http://mirror.hetzner.de/ubuntu/packages focal-backports InRelease
Hit:4 http://mirror.hetzner.de/ubuntu/packages focal-security InRelease
Hit:5 http://download.virtualbox.org/virtualbox/debian hirsute InRelease
Hit:6 http://de.archive.ubuntu.com/ubuntu focal InRelease
Hit:7 http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu focal InRelease
Ign:8 http://linux.dropbox.com/ubuntu disco InRelease
Hit:9 http://de.archive.ubuntu.com/ubuntu focal-updates InRelease
Hit:10 http://linux.dropbox.com/ubuntu disco Release
Hit:11 http://de.archive.ubuntu.com/ubuntu focal-backports InRelease
Ign:12 http://ppa.launchpad.net/x2go/saimaa/ubuntu focal InRelease
Err:13 http://ppa.launchpad.net/x2go/saimaa/ubuntu focal Release
404 Not Found [IP: 2620:2d:4000:1::3e 80]
Hit:14 http://security.ubuntu.com/ubuntu focal-security InRelease
Hit:15 https://esm.ubuntu.com/infra/ubuntu focal-infra-security InRelease
Hit:16 https://esm.ubuntu.com/infra/ubuntu focal-infra-updates InRelease
Reading package lists... Done
E: The repository 'http://ppa.launchpad.net/x2go/saimaa/ubuntu focal Release' does not have a Release file.
N: Updating from such a repository can't be done securely, and is therefore disabled by default.
N: See apt-secure(8) manpage for repository creation and user configuration details.
N: Skipping acquire of configured file 'non-free/binary-i386/Packages' as repository 'http://download.virtualbox.org/virtualbox/debian hirsute InRelease' doesn't support architecture 'i386'
N: Skipping acquire of configured file 'contrib/binary-i386/Packages' as repository 'http://download.virtualbox.org/virtualbox/debian hirsute InRelease' doesn't support architecture 'i386'
root@noc /var/log/apt #
##################

In the end:

##################
root@noc /var/log/apt # systemctl status x2goserver.service
● x2goserver.service - LSB: Start and stop the X2Go daemon
     Loaded: loaded (/etc/init.d/x2goserver; generated)
     Active: failed (Result: exit-code) since Wed 2023-05-31 13:57:11 CEST; 24h ago
       Docs: man:systemd-sysv-generator(8)
    Process: 2000 ExecStart=/etc/init.d/x2goserver start (code=exited, status=127)

May 31 13:57:11 noc systemd[1]: Starting LSB: Start and stop the X2Go daemon...
May 31 13:57:11 noc x2goserver[2000]: * Cleaning up stale X2Go sessions
May 31 13:57:11 noc x2goserver[2000]: /etc/init.d/x2goserver: 26: x2gocleansessions: not found
May 31 13:57:11 noc systemd[1]: x2goserver.service: Control process exited, code=exited, status=127/n/a
May 31 13:57:11 noc systemd[1]: x2goserver.service: Failed with result 'exit-code'.
May 31 13:57:11 noc systemd[1]: Failed to start LSB: Start and stop the X2Go daemon.
##################

And also:

##################
root@noc /var/log/apt # sudo apt-get install x2goserver x2goserver-xsession
Reading package lists... Done
Building dependency tree
Reading state information... Done
You might want to run 'apt --fix-broken install' to correct these.
The following packages have unmet dependencies:
libx2go-log-perl : Depends: x2goserver-common (>= 4.1.0.4-0~1975~ubuntu20.04.1) but 4.1.0.3-5 is to be installed
libx2go-server-db-perl : Depends: x2goserver-common (>= 4.1.0.4-0~1975~ubuntu20.04.1) but 4.1.0.3-5 is to be installed
libx2go-server-perl : Depends: libx2go-log-perl (< 4.1.0.3-5.1~) but 4.1.0.4-0~1975~ubuntu20.04.1 is to be installed
Depends: libx2go-server-db-perl (< 4.1.0.3-5.1~) but 4.1.0.4-0~1975~ubuntu20.04.1 is to be installed
E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).
root@noc /var/log/apt #
##################

So we're still stuck. Any further help would be greatly appreciated. Thanks in advance.