Expose your own long-running work as an async API. The caller POSTs, gets a job id back in milliseconds, and the answer is pushed to a realtime channel when it lands, with a status route as the fallback. Nothing holds a request open, so work that outlives a proxy timeout still completes and is still retrievable. SQLite, so it runs with nothing installed.
The Postgres build of Async Job API: the same submit-then-push job API, on a database that handles concurrent writers. result is jsonb so outcomes are queryable, jobs are indexed by owner, and the status response carries elapsed time. Use this one to deploy; the SQLite sibling exists to be run with nothing installed.
Wait for a long-running job without holding a request open. Submit the work, poll until it reports done, and suspend the run between polls so nothing is held open and a restart does not lose it.