Is it possible to build a GitHub App that takes actions on behalf of my user account?
Technically, yes, you can do this, but it’s not the typical use case. When GitHub Apps take action through GitHub, they act as bot users. By contrast, OAuth apps take action as user accounts, known as machine accounts. (Check out the differences between machine and bot accounts here.)
It is possible for a GitHub App to act on behalf of a user using a user access token, with very limited access. We call these user-to-server requests. You can find the list of supported endpoints here.