Function notify_password_managed_with_retry 

pub async fn notify_password_managed_with_retry(
    tmc_client: &TmcClient,
    upstream_id: String,
    user_id: Uuid,
)

Notify TMC that a user’s password is now managed by courses.mooc.fi.

This is best-effort and never fails the caller: by the time it runs the password has already been stored locally, so a transient TMC outage must not turn a successful signup/login/migration into an error. It retries a few times inline (so common blips are resolved before the HTTP response) and, if those are exhausted, hands off to a background task that keeps retrying with backoff.