can one airtag be connected to more than one apple id?

No.

From: 'How to reset your AirTag' --> https://support.apple.com/HT212251

"An AirTag can be associated with one Apple ID. If you want to use an AirTag that someone else has used, they need to remove the AirTag from their Apple ID first. "

We are thinking about actually using an old iPhone with a newly created Apple ID for the cat and bind the airtag to that Apple ID. A cat with her own iPhone 😂.

No, just put two Airtags on the cat.

What if it was a dog?

Well, that's disappointing. My wife and I have one car, so it would be nice for us both to be able to track the keys.