It is not a theme issue (looks for me), as I tried on default (19), Genesis, OceanWP, GeneratePress and Astra.
So, to repeat, I consider it MetaBox issue as:
1) I checked on right metabox that I want to associate categories and tags to my CPT.
2) Code (PHP) is wrote that action in order.
3) Custom Categories created by MB can be listed (displayed).
4) Custom 'tags' (non hierarchical taxonomy) created by MB can be listed (displayed).
SOLUTION
So, I simply deactivated Categories and Tags, plus created replacements by MB and it works. However, it is not a topic, as I ask why it not working?
By the way, your new versions have a bug on repeated License requests and boxes.