I found the app transfer process to be fairly straightforward.
After an app transfer:
The app is transferred to your dev account
The Bundle ID stays the same (and becomes yours)
The App ID Prefix changes (from the previous developer's Team ID, to your Team ID)
Xcode
Signing & Capabilities:
"Team" should show your dev Team
"Bundle identifier" should be the same as before the transfer
Nowadays, I generally let Xcode automatically handle all of the Certificate/Profile side of things, but you can still do it manually, if you prefer.