Dear Stefan, first of all thanks for having suggested some path to follow.

See here:

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root@noc /var/log/apt # apt full-upgrade -d
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 installed
 libx2go-server-db-perl : Depends: x2goserver-common (>= 4.1.0.4-0~1975~ubuntu20.04.1) but 4.1.0.3-5 is 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 installed
                       Depends: libx2go-server-db-perl (< 4.1.0.3-5.1~) but 4.1.0.4-0~1975~ubuntu20.04.1 is installed
E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).
root@noc /var/log/apt #
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So that is a dead end. And "apt --fix-broken install" is just the same:

########################################################
root@noc /var/log/apt # apt --fix-broken install
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Correcting dependencies... failed.
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 installed
 libx2go-server-db-perl : Depends: x2goserver-common (>= 4.1.0.4-0~1975~ubuntu20.04.1) but 4.1.0.3-5 is 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 installed
                       Depends: libx2go-server-db-perl (< 4.1.0.3-5.1~) but 4.1.0.4-0~1975~ubuntu20.04.1 is installed
E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.
E: Unable to correct dependencies
root@noc /var/log/apt #
########################################################

Now see here:

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root@noc /home/desktop/Desktop # grep -r x2go /etc/apt/sources.list*
/etc/apt/sources.list.d/x2go-ubuntu-stable-focal.list:deb http://ppa.launchpad.net/x2go/stable/ubuntu focal main
/etc/apt/sources.list.d/x2go-ubuntu-stable-focal.list:# deb-src http://ppa.launchpad.net/x2go/stable/ubuntu focal main
########################################################

So we're actually using X2Go stock from the Ubuntu repositories.

And with regards to how the mess has happened, history.log was actually/already rotated, and this is what I see, after having grepped /var/log/apt/history.log.1.gz, looking for "x2go" recurrences:

########################################################
Start-Date: 2023-05-31  09:28:30
Commandline: packagekit role='update-packages'
Requested-By: desktop (1000)
Upgrade: iptables:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), x2goserver-x2goagent:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), openssl:amd64 (1.1.1f-1ubuntu2.18, 1.1.1f-1ubuntu2.19), snapd:amd64 (2.58+20.04, 2.58+20.04.1), libip6tc2:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), libxtables12:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), x2goserver-common:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), libx2go-server-perl:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), libssl1.1:amd64 (1.1.1f-1ubuntu2.18, 1.1.1f-1ubuntu2.19), libip4tc2:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), tzdata:amd64 (2023c-0ubuntu0.20.04.1, 2023c-0ubuntu0.20.04.2)
Remove: libx2go-utils-perl:amd64 (4.1.0.3-5)
Error: Sub-process /usr/bin/dpkg returned an error code (1)
End-Date: 2023-05-31  09:28:30

Start-Date: 2023-05-31  09:28:52
Commandline: packagekit role='update-packages'
Requested-By: desktop (1000)
Upgrade: iptables:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), openssl:amd64 (1.1.1f-1ubuntu2.18, 1.1.1f-1ubuntu2.19), snapd:amd64 (2.58+20.04, 2.58+20.04.1), libip6tc2:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), libxtables12:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), x2goserver-common:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), libx2go-server-perl:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), libssl1.1:amd64 (1.1.1f-1ubuntu2.18, 1.1.1f-1ubuntu2.19), libip4tc2:amd64 (1.8.4-3ubuntu2, 1.8.4-3ubuntu2.1), tzdata:amd64 (2023c-0ubuntu0.20.04.1, 2023c-0ubuntu0.20.04.2)
Remove: libx2go-utils-perl:amd64 (4.1.0.3-5)
Error: Sub-process /usr/bin/dpkg returned an error code (1)
End-Date: 2023-05-31  09:28:52

Start-Date: 2023-05-31  09:34:27
Commandline: /usr/sbin/synaptic
Requested-By: desktop (1000)
Upgrade: x2goserver-x2goagent:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), x2goserver-common:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), libx2go-server-perl:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1)
Remove: libx2go-utils-perl:amd64 (4.1.0.3-5)
Error: Sub-process /usr/bin/dpkg returned an error code (1)
End-Date: 2023-05-31  09:34:27

Start-Date: 2023-05-31  09:43:08
Commandline: apt --fix-broken install
Requested-By: desktop (1000)
Upgrade: x2goserver-common:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1), libx2go-server-perl:amd64 (4.1.0.3-5, 4.1.0.4-0~1975~ubuntu20.04.1)
Remove: libx2go-utils-perl:amd64 (4.1.0.3-5)
Error: Sub-process /usr/bin/dpkg returned an error code (1)
End-Date: 2023-05-31  09:43:09
########################################################

In the end: the origin of the problem was caused by Discover automatic updates. I authorized those packages to be updated, and soon after this is what I got:

After first errors - from inside Discover itself - we got this also (the client-side suspension was not effective at all).

And now, if we try to re-connect:

Thanks for further suggestions, if any, and best regards, e.-