Mint a short-lived URL for a recording hosted by the telephony provider.

Only available for calls whose provider supports minting (TCN today; 404 for providers that don't, e.g. awsconnect refs deep-link to the Connect console instead). The URL expires after ~10 minutes, so it is minted per request and must not be cached beyond that. Returns 409 while the provider is still processing the recording (it lands a few minutes after hangup).

Deliberately holds no request-scoped DB session: the provider HTTP round-trip can hang for minutes, and a request cancelled mid-await with a checked-out connection is the Sentry "garbage collector cleaning up non-checked-in connection" signature.