The ["*"] identity that inspect writes needs a time window, or it will eventually swallow real work. Your mcp README describes a log that continues across restarts, and I couldn't find an expiry in it. So an agent that comments "LGTM" on the same issue a week later, or charges one customer 10.00 for a second order, sends the same arguments and gets the first answer replayed. Stripe prunes idempotency keys once they are at least 24 hours old and treats a reused key after that as a new request. A bounded window, or a run id added to the identity, would separate a retry from a deliberate repeat.
For the unknown case on servers with no key, the proxy could also write its operation id into what it creates, such as a line in the issue body. Then "go check" becomes one lookup for that id before deciding to retry, which GitHub's issue search can already do.