It looks like they removed the Paint3D "Open with" entries in the recent release. Adding the entry manually via the registry doesn't seem to work.
Please submit feedback to Microsoft via the Feedback Hub (Win + F).
Also, I suggest upvoting these threads at the Feedback Hub, if possible.
By the way, the earlier version (2310.24037.0) doesn't have this problem. You can download it from the Microsoft servers via the Microsoft Store - Generation Project: https://store.rg-adguard.net/
On the above portal, paste the following URL and generate the Appx download links for Paint 3D.
- https://apps.microsoft.com/detail/9nblggh5fv99 (Paint 3D - Microsoft Store URL)
(After installing the older version, turn off the auto-updation of Store apps. Otherwise, the app will be updated to the latest version.)