It depends. It always depends.
In my case, I’m keeping the SAME database, so I can’t really change the model without changing the past versions. That’s why I have the versioned APIs on the Resource instead of the Controller or Model.

Keeping two git branches is keeping two different projects, processes deployed. You need to structure your whole app to have two Laravel apps serving in the same domain but different sub URLs.
I think you need to ask the right question or read again this approach.