Modified GitHub sign out behaviour when hosted in an app

Is your feature request related to a problem? Please describe.
I'm working in the iOS app to support the GitHub integration by stopping the GitHub URLs being opened in Safari.

When signing out of GitHub in the app, "are you sure" can only make sense if it's about MakeCode signing out. Going back from the "are you sure" page leaves me unable to logout without logging in again, and any subsequent user will get logged into my account.

In the iOS app's webview, logging in and out of github doesn't seem to affect github or MakeCode in the browser. When signing out of MakeCode, there are no other tabs in the app needing a github connection.

Describe the solution you'd like
When hosted in a web view, can logout bypass the "are you sure" prompt?

Alternatively, could MakeCode keep its token intact until it gets a message from the webview app to stay the user has logged out (the app can see the change from /logout to /). Either would make more sense to a user that doesn't understand the details of what's happening.

Describe alternatives you've considered
Open the logout page in a hidden view and fake a tap on the button?
Intercept the sign out menu entries, to save and restore local storage?

Additional context
Previously mentioned in https://github.com/microsoft/pxt-microbit/issues/3039.

Start by tracing the GitHub logout flow in the iOS web view, including the transition from /logout to /. Compare the web-view behavior with MakeCode sign-out and determine which behavior should be treated as done: bypassing the confirmation prompt or preserving the token until the app reports that the user logged out.