How to create language templates in 2022 theme

I’ve been using Polylang for years on various sites without issues.

However, I just switched to the twenty twenty-two theme with its Full Site Editor and site templates and template parts.

Is Polylang currently not compatible yet with FSE?

I have created translated header and footer template parts (menus, etc) for each language and assigned them to a corresponding site template (Single Post, Homepage).

However, that doesn’t work.

It seems to me you can only have one site template for the Homepage active?

Thanks!