I was using X2Go succesfully on my Xubuntu laptop, but after running apt upgrades it is all screwed up and I can neither use it nor purge it, nor use APT for anything else.

Same here, as per previously posted messages:

https://lists.x2go.org/pipermail/x2go-user/2023-May/006999.html
https://lists.x2go.org/pipermail/x2go-user/2023-May/007000.html
https://lists.x2go.org/pipermail/x2go-user/2023-May/007001.html

Mihai replied:

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You won't be able to upgrade X2Go packages just yet. The new version of X2GoServer depends upon KDrive components that are currently unreleased, so you'll have X2Go Server subpackages that won't be upgradeable. I have to throw out a barrage of other releases to bring this into an consistent state, but that will probably not be finished until the end of this week or next week (just because it's a lot of work and requires a lot of testing and building).
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This seems to be kinda annoying, anyway.