I have essentially same problem, but iPhone 13, both Mac and phone have most recent update Mont 12.6 and 16.0.2. Since put 16.0.2 on phone twice now I have hit the device not found on the Mac to update. Last time I bricked it and restarted from the iCloud backup, and then the Mac could see it again. But the reloading of the phone is a pain as It takes about 12 hours to load everything back onto phone. Now I have to do this again.
Is this a feature of having to much on the phone? I have about 500gig of mp3 on it but that said I have had that for awhile and its a new problem. And yes I have used different cords, it charges fine, just doesn't sync