Github App access user project board

Is it possible to give a Github App access to a user Github Project board?

I’m attempting to experiment with having a Github App automate cards across a Github Project board.
Whilst eventually this would be used on an organisation board, for now I’m testing on my user board. I’m unable to have the Github App access the project board and am unsure if it’s because I missed something or it’s not currently possible.

Under permissions for the App I can see that I can add Project permissions for “Organization permissions”, but can’t see the same option in “User permissions”.
I’ve added the Organization access, but that hasn’t helped.

When attempting I get the error:

RequestError [HttpError]: Resource not accessible by integration

When attempting to call with Octokit

octokit.rest.projects.listForUser({ username: "MY_USERNAME" });

Any help will be very appreciated, even if it’s just to confirm that this isn’t available in the current preview. If it’s not possible I can always setup an organisation for testing as a workaround.