If you are seeing this error when trying to kick off a new EAS build of your Expo app, that means your Apple ID's API access has been locked. It's not a timeout that goes away automatically — you will have to manually unlock it.
Do not remove your ~/.app-store directory or touch any files, as that's just going to make your life harder.
You can go to iforgot.apple.com and unlock it without resetting your password. Just follow the prompts like you would for a password reset. The unlocking flow will kick in and you will have to approve on one of your devices.

After you see this screen and approve the unlock, that's it. You can go back to using EAS without any issues.