Does the Advanced Booking Calendar work with pure FSE (Gutenberg) themes

I tried to use the Advanced Booking Calendar plugin on a pure FSE Theme, like the “Twenty Twenty-Two” and there the plugin does not work. Especially the “Verfügbarkeit Prüfen”( check available rooms) Butten does not work at all. I found that other functionalities also have issues.

So it looks like that this plugin has some problems when used on FSE (Full Site Editing) themes.