Thanks for the explanation. I guess it was a problem with Baïkal after all.
I have “fixed” it by switching to DAViCal.
Very intimidating documentation & UI, but almost nothing needed to be configured and it Just Worked.
So,DAViCal is the server DAVx5 syncs everything on Android on the desktop I use vdirsyncer & khal for the calendar only (vdirsyncer still refuses to sync my contacts), and SoGo connector for contacts on thunderbird.
It’s been a long day.