I have the same problem. I support my family with a total of 6 different Mac computers and it's the exact same situation, it's a bug introduced with Ventura 3.1.
I called Applecare tech support and after 1.5 hours on the phone and doing typical level 1 followed by level 2 support diagnostics over a 2 hour period, I was told that this situation is a known problem at Apple and that it will be fixed eventually.
The default browser works for links within Emails, however it doesn't work from desktop URL shortcut (.webloc) files.
The only workarounds are to drag/drop the .webloc shortcuts into the desired browser and/or setup shortcuts within the browser shortcut bar.