Error 121: "The semaphore timeout period has expired" is a network related error, not a SQL Server timeout. The source of the issue can be related to your VPN if you are using a VPN or to Network connectivity problems
Network connectivity problems have various causes, but they typically occur because of incorrect network adapters, incorrect switch settings, faulty hardware, or driver issues. Some connectivity symptoms are intermittent and do not clearly point to any one of these causes.
You can get more information in this post: https://mskb.pkisolutions.com/kb/325487
Note: You can increase the time-out setting value of the SSMS connection configuration. This will solve the issue but will bypass it in some cases.
Note! I do not remember that I got this error when using Azure SQL managed instance but as mentioned it is known when using on-premises server as related to Network connectivity problems