I've experienced before where the QR code resolves to a URL that only works once to return the secret to the app, I found this rather annoying since my use case was trying to sign up to a MFA and save to a yubikey and phone, and it consequently didn't work.

IIRC the QR code can either embed the TOTP code itself, or a url that returns it, that url can be a one time access thing, in which case you'll have to rely on another process to extract the TOTP and share in multiple readers

Forget the service in question