Cat doorbell

OP - Do you mean some device that will tell you when your cat is at the door when you are coming in so that he/she does not run out - not meaning to run out, but just interested? If that is the case all I can recommend is to be very, very careful when coming in the door. That is what we do with our white cat and a white door. Used to have a white dog with the same white door. Dogs at least are easier to catch - well some are, some think it is a game.

Outside of a heat sensor of course if that even exists.

If you let your cat out and it wants to come back inside, and usually waits by the backdoor, you can set up a camera, like a wyze cam, narrow the motion sensor window to where the cat usually waits to be let in, and when the cat is in the motion sensor area, it will send a notification to your phone.