@robi I measured again and it look 30-50 seconds. With the default
pool_timeout of 50 that should suffice, yet when I tried multiple times with the defaults it never succeeded. It's possible that it was always close.
I have tried to reach out to their IT support, because at first I thought it's a bug on their end. Their response was that they don't see anything wrong on their end. It's also a prospective business customer/partner, so my interest in the ability to exchange emails with them outweighs theirs for sure at this stage. Consequently I'd rather apply generous timeouts than ask their IT to make changes