I haven’t tried to replicate the issue yet, but have you re-saved your permalinks after adding the CPT?
That might solve the “invalid post type” error. Please let me know if it helps, otherwise I’ll investigate deeper.
I have spun up a couple of new sites and not getting this error. There is 1 site that is still causing problems but i suspect it is something with a plugin. Getting lots of errors on this site tbh so it could be anything.
Happy for this to be marked as no bug though as a new clean install is working as intended.