It's most likely a session lock.
If the handler of the first request uses the session, then all other requests whose handlers also use the session will wait for the first one to complete.
You can try using the session_write_close() function in the long handler.
It will write to the session and end it.
You can also consider queues as a solution to your problem.
It looks like:
(request -> do something -> put job with payload to queue -> response ) <- quick request
(queue daemon -> get job -> execute -> await new job) <- long hard work