I’ve managed to bug it out (after deleting WP transients and all taxes from the status menu, likely not related, but trange notheless). going to the setup wizard via the WP dashboard then worked, but tried to force my theme to 2024. Does this plugin require integration with a theme? Most others will allow simply adding products to pages and posts.
Edit: After changing the theme back (as this is a production site and that is not something that should be changed (especially arbitrarily by a plugin!)) the problem returns. I did not have time to test if this also fixed the block editor on posts that have nothing to do with the plugin, but I would assume not.