You can have a separate GitHub account for your agent (GitHub ToS actually allows that since April) and that account can fork your repo and open PRs. This way it cannot do any real damage but can still push.

See this user for example: https://github.com/filippo-agent

https://docs.github.com/en/site-policy/github-terms/github-terms-of-service#3-account-requirements

3. Account Requirements

We have a few simple rules for Accounts on GitHub's Service.

You must be a human to create an Account. Accounts registered by "bots" or other automated methods are not permitted. We do permit machine accounts:

A machine account is an Account set up by an individual human who accepts the Terms on behalf of the Account, provides a valid email address, and is responsible for its actions. A machine account is used exclusively for performing automated tasks. Multiple users may direct the actions of a machine account, but the owner of the Account is ultimately responsible for the machine's actions. You may maintain no more than one free machine account in addition to your free Personal Account.

One person or legal entity may maintain no more than one free Account (if you choose to control a machine account as well, that's fine, but it can only be used for running a machine).