[Antithesis] Move initial Get request to a separate step

### What would you like to be added?

We could do it in entrypoint before emmiting setup complete to avoid separate binary.

We should report for this single client so it can be picked up by singleton execution later.

### Why is this needed?

This should increase effective time of Antithesis testing.

Start at the entrypoint mentioned in the issue and trace how the initial Get request and setup-complete signal are handled. Determine how to report the single client for later singleton execution, then verify that Antithesis testing gains effective time without requiring a separate binary.

Written by the indexing model from the issue text.