[Examples] [Async Handlers] simplify code by splitting long_async_handler into two functions (IDFGH-14011)

[chipweinberger]

I originally wrote this example, but made it too complicated.

I don't know what I was thinking. I was calling long_async_handler twice, and used a is_on_async_worker_thread to do different behavior depending on which thread you are on.

This is needlessly complicated.

It's much simpler to have two functions:
long_handler - called on http thread
long_async - called on async thread.

This leads to much more straight forward code.

I also simplified some variable names.

[github-actions]

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