Hi,@HSB Welcome to the Microsoft Q&A forum thanks for posting your question.
If I understand correctly you are having trouble connecting to an Azure SQL Managed Instance from home using SSMS while connected to their office network via VPN
When connected through VPN it's possible that a different IP address is used for egress, and it's possible that your traffic to Azure public IPs doesn't even traverse the VPN. The error message should tell you the IP address your connection attempt appears to be coming from. 10060 error can occur due to various reasons, including network connectivity issues, firewall settings, or incorrect login credentials.Check the IP address used for egress when connected through VPN.also check if your firewall is blocking traffic.
Regards
Geetha