I had the very same issue however I updated to Monterey 12.6 and when it was finished safari wouldn't open and gave me an error message that read safari isn't supported by this Mac. I was like what?? so I got on google chrome and searched for answers.
went to apple support and even chatted with support. he told me to go into safe mode to see if I still had the issue and of course I did. and went back to support and another one asked me if I looked for an update lol hello I just downloaded the latest software Monterey 12.6 and yes the safari come with it and its not in the App Store. so finally I just did what any old windows boy would have done I went and reinstalled the Monterey 12.6.
I now have an update for safari which I haven't yet done but if I do I will know how to go back cause my safari right at this moment is working fine after the twelve hours of waiting on the restore/install of Monterey.
if you know how to get to the reinstall portion of this machine than you should be good to go..
I followed these instructions for my issues and wished the support team knew that this will fix safari back to version 15.6.1
now this was tricky cause I'm not easy with directions and read into stuff and have a logi mx keyboard so I had to get out my key board that come with the Mac. good luck and hope it helps it did for me..
warning this will take hours I started at around 10am and it just finished around 8pm
Restore Mac
- Press the power button and hold down ⌘ + R.
- Release ⌘ + R when you see the Apple logo or a spinning globe.
- Type your admin username and password, if prompted.
- Go to macOS Utilities.
- Choose install MacOS Monterey