Thanks Vladislav Hrdina
Glad to know that you were able to figure this out and thanks for sharing the rootcause. By the way, Microsoft Q&A community has a policy that "The question author cannot accept their own answer, they can only accept answers by others.". Hence request you to accept this as an answer so we can close this thread. I am summarizing the issue and root cause you have found for it.
Issue Summary: After reinstalling Windows 11, I can't connect to the database via SQL Server Management Studio using Microsoft Entra MFA, though Azure Data Studio works fine with the same credentials.
Fix: Resolved the issue by creating a local profile for the Lieberman account, switching the default browser to Chrome, which successfully loaded the database page.