Hi there,
After debugging both versions again, I found the cause of the problem.
zoom-instant-sdk:
Since a session object was returned, I already suspected that it had another cause. Googling shows that the code 5003 in the zoom client indicates a connection problem. It would still be great if you could confirm this error detail code for the Video SDK.
Since then I have not gotten the error. I guess that was an unfortunate coincidence. Sorry about the confusion.
zoom-video-sdk:
I had noticed before that the user_identity in JWT is limited to 16 characters. (see customUserId property does not exist - #8 by blindgaenger)
Since “zoom-video-sdk-iOS-1.1.0” the limit has strangely decreased to 15 characters.
"user_identity": "1234567890123456", ← works in 1.0.2, but fails in 1.1.0
"user_identity": "123456789012345", ← works in both versions
This is a pity, because I use UUIDs as user IDs, and the customUserId cannot be set yet. I would have liked the limit to increase. 
Anyway, the solution is obvious, so I mark this thread as solved.
Cheers,
Bernd