Apart from Xbox Live, I can't connect to any of the integrations listed below that. See attached screenshot.

Please fix it.

And who should fix this? Those integrations are made by community, not by GOG.
Try to update them with this https://github.com/Slashbunny/gog-galaxy-plugin-downloader

If Retry doesn't work, close Gog Galaxy and go to %LOCALAPPDATA%\GOG.com\Galaxy\plugins\installed\twitch_8b831aed-dd5f-c0c5-c843-41f9751f67a2

In that folder, delete all the integration folders (steam, uplay, etc.).

Restart gog and it "should" work. Nothing guaranteed though, steam doesn't work for me this last week. From the plugin you linked "GOG Galaxy client automatically downloads and updates plugins from within the Integrations screens. You should install plugins using GOG Galaxy itself, not this software." They say to not use this software anymore

And who should fix this? Well, the main marketing point of Gog Galaxy 2.0 is their integrations lol
A nice way to wash their hands indeed but in all honesty they should be responsible for them, don't you think?

Yes, they say it, but I still used it and it hepled. And it indeed updated my steam plugin.
No, I don't think so. They only responsible for xbox plugin, others a community made, made by another people. They can work with them, trying to optimize, fix something and other stuff, but responsible? Nope. And its not the way to wash their hands, they got no legal agreement with Steam and other platforms, only with Microsoft.