Only one simultaneous connection per user?
Is there any way such a connections-per-user limitation may have been defined on the database, and if so, how can I turn it off?


You are using Microsoft SQL-Server. You can limit the Resources with the Resource Governor. Have a look at the Microsoft Documents. There you can see which options might be set and you should check. If there is a limitation, you may find it there.

Documentation: https://docs.microsoft.com/en-us/sql/relational-databases/resource-governor/resource-governor