How can I manage git for my strapi app?

So the idea is to have one source of truth.
Which in this case is your local branch.

If you do changes you are right you do them locally then push them to the servers.
The servers pulls the changes and restarts the server and the changes then gets applied to the database.

Everytime strapi “Starts” it does a sanity check for tables and rows and also checks the schema files for changes.