I wrote a block entry about the fix: https://auri.net/2025/08/28/fixing-testflight-error-couldnt-load-apps-testflight-is-currently-unavailable/

If your device is using a managed identity - such as a corporate account / SSO - you need to be added to the Apple account for this to work. I'll write an article about this. What a nightmare. Apple should have better error messages.