Thank you for the additional investigation @deepinart 
Your mention of an Illustrator-only issue reminded me of a topic recently discussed here on the forum: Problem auto-activating Illustrator 29.3.1 on Mac (Intel)
Would it be possible for you to try the workaround mentioned in the initial message there and see if that would make a difference? This would really help in trying to understand if the cause of the issue is the same.
Thank you again,