Seems there was a separate update for Safari ie: 16.5.1 alongside the MacOS 12.6.7 update.
If you haven't already downloaded that Safari version:
Try Apple Menu > About this Mac > Software updates >
See "other updates available" and click on "More info". to go to the small window with the Safari update.
Else:
If you already downloaded that version:
Wondering if you have any third-party (non-Apple) apps such as ad-blockers, unneccessary virus-checkers, cleaners etc., installed as they can be the cause of difficulties ... try turning off any such apps, (and even VPN) and check if you can use Safari.
(You can generally use uninstallers from the developers if any are found to be interfering.)
also:
What to do: If your Mac isn't connecting to the internet over Wi-Fi - Apple Support
Seems we can not uninstall / delete / restore / any of Apple's in-built apps on Mac.
What to do: If an app on your Mac stops responding, closes unexpectedly, or won’t open - Apple Support
and
For App store apps: Uninstall apps on your Mac - Apple Support
More support if needed: Contact - Official Apple Support
All the best :-)