Welcome to Microsoft Q&A forum.
As I understand, you are unable to connect to Azure Data Studio due to connection time out.
Could you please let us know if it was working fine earlier? If it was working fine, please try to update Azure Data Studio to the latest version and see if the issue resolves.
Also refer to the https://techcommunity.microsoft.com/t5/azure-sql-blog/troubleshooting-problems-related-to-azure-ad-authentication-with/ba-p/1062991 here which might help in troubleshooting.
Also if above does not help, I will suggest you to raise question over https://github.com/microsoft/azuredatastudio/issues
so that concerned team can help.
Thanks