Custom posts not visible anymore after WP update

I just updated my website to WordPress 5.6 (from 5.5.1) and now apparently my custom types have been messed up in the database. Essentially, I have one custom post type (“buecher”) which I will insert into pages based on categories. The page https://www.flamel-forum.eu/die-buecher/die-geheimnisse-des-nicholas-flamel/ eg includes “latest posts” from custom post type “buecher”. While these posts are shown nicely in the preview, when clicking on them the post appears not to be found (eg https://www.flamel-forum.eu/buecher/der-unsterbliche-alchemyst/). The posts do appear in the search. The categories that contain the posts are also not available (eg https://www.flamel-forum.eu/category/buecher-uebersicht/). What should I do? I have a backup from before the update, but I would prefer to keep WP 5.6.

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