Making a git commit typically doesn't require any special permissions or credentials since it's all local to the machine. You could do something like running the agent as a different used and carefully setting ownership on the .git directory vs. the source code but this is not very straightforward to set up I suspect.
Typically agents are not operating as a distinct user. So they have the same permissions, and thus credentials, as the user operating them.
Don't get me wrong, I find this framework idiotic and personally I find it crazy that it is done this way, but I didn't write Claude Code/Antigravity/Copilot/etc