Whenever my iPhone 13pro loses mobile signal, it goes into SOS only mode, but does not reconnect to signal once I’m back in coverage area without having to manually reset phone.

If you see No Service or Searching in the status bar on your iPhone or iPad (Wi-Fi + Cellular), your device isn't connected to a cellular network. If you see SOS or "SOS only" in the status bar, your device can still make emergency calls.

If you see No Service, Searching, or SOS on your iPhone or iPad

I had this problem once. Someone told me it was an issue with the sim card. After I went to the store and got a new sim card, it worked fine.