Describe the task you're waiting for as text, and let an LLM pick the number of seconds for each request. More expensive the better model you clearly need for this. There, your AI pitch.
Retries won’t work in that case. Would be better to have two endpoints: get the time in x seconds and wait until time passed. That way retrying the wait endpoint will work fine and if time hasn’t elapsed it can just curl itself with the same arguments.