Hi @Audrius Welcome to the Microsoft Q&A forum, Thanks for posting your question.
It's possible that the maximum number of connections is not being updated after you upgraded your plan. Have you tried restarting the Azure Postgres server to see if the new maximum connection limit is applied?
Can you share the result for this SHOW max_connections;
you can also change the max_connection from server parameters as shown below
Regards
Geetha