In the old days the check whether MP3tag actually goes into the internet was to use Help>Check for new version ...
You should get a message box.
If you don't then MP3tag has no internet access.
You would have to check locally then, why this is the case.
I'm using Windows 11 25H2 26200.8737 and I'm not experiencing those timeout issues, so it's unlikely to be related to Windows 11 build 26200 or a recent WinINet change.
If this results in a timeout or a 12002 error, it strongly suggests that WinINet is malfunctioning on your system.
BTW: What build exactly do you use? My Windows 11 shows version 25H2 26200.8655 (using the command winver.exe), which is a stable, non-preview release updated to date.
A 301 result is good (it means "HTTP 301 Moved Permanently" and is the answer from the reached external server).
What about security software in your environment?
Could you disable all your antivirus, firewall and other protection software - just for a test in Mp3tag with MusicBrainz and Discogs?
This would allow us to rule out any influence they might have.
If you stop AVAST for 10 minutes, and then immediately try to connect to MusicBrainz and Discogs in Mp3tag, does it work? (Connecting with paused AVAST?)