Update: iTunes 12.6.5.3 sees the iPhone 6s with iOS 13 done via OTA on Mojave as well.
Today I got an alert on both systems, while yesterday everything was working without the update.
"Software update is required to connect to your iOS device" on your iPhone, iPad, or iPod touch"
I didn't know if it was going to mess up the old iTunes or my old iPhone 6s.
I had to do it at least on HighSierra and it works., but syncing the iPhone with new apps doesn't work automatically, you need to update the apps manually via iTunes ? or through App store on iPhone .
I need to verify with other apps though, and will in the next days. Everything else is syncing
Sync tab still works but doesn't update the date under Backup Now: if you want to know the real syncing date you need to do a Backup Now
I remember a long time ago we had a similar issue with iTunes, solved by a new release: I'm afraid will have to keep it that way now, sigh