Seems OK via the browser (hit next to load a few pages). Might be the app, or the Jerboa app (0.0.52) interacting with the new server weirdly? I may try a full re-install just to be thorough.
Edit: tried a full uninstall, reinstall, and login. Same issue on my end. I suppose it may be better to try and attack this from the Jerboa side.
I prefer not to sync my information with Google or other entities either, but do not think that using Linux precludes using whatever tools they like. I don’t think this is a question about ideals, but about tools and compatibility.
I personally also doubt that Google Tasks supports that capability, unfortunately. I personally use Thuderbird for email on Linux, and it supports tasks too (I use Nextcloud for my tasks but I bet it supports Google as well). Not the same as your gnome extension, but an option.
Good luck!