gh-138122: Make sampling profiler integration tests more resilient

[pablogsal]

The tests were flaky on slow machines because subprocesses could finish
before enough samples were collected. This adds synchronization similar
to test_external_inspection: test scripts now signal when they start
working, and the profiler waits for this signal before sampling.

Test scripts now run in infinite loops until killed rather than for
fixed iterations, ensuring the profiler always has active work to
sample regardless of machine speed.

• Issue: Implement PEP 799 – A dedicated profiling package for organizing Python profiling tools #138122

[bedevere-bot]

🤖 New build scheduled with the buildbot fleet by @pablogsal for commit 56f0d93 🤖

Results will be shown at:

https://buildbot.python.org/all/#/grid?branch=refs%2Fpull%2F142382%2Fmerge

If you want to schedule another build, you need to add the 🔨 test-with-buildbots label again.

[bedevere-bot]

🤖 New build scheduled with the buildbot fleet by @pablogsal for commit 56f0d93 🤖

Results will be shown at:

https://buildbot.python.org/all/#/grid?branch=refs%2Fpull%2F142382%2Fmerge

If you want to schedule another build, you need to add the 🔨 test-with-buildbots label again.

[bedevere-bot]

🤖 New build scheduled with the buildbot fleet by @pablogsal for commit 1682b1a 🤖

Results will be shown at:

https://buildbot.python.org/all/#/grid?branch=refs%2Fpull%2F142382%2Fmerge

If you want to schedule another build, you need to add the 🔨 test-with-buildbots label again.

[bedevere-bot]

🤖 New build scheduled with the buildbot fleet by @pablogsal for commit 4599726 🤖

Results will be shown at:

https://buildbot.python.org/all/#/grid?branch=refs%2Fpull%2F142382%2Fmerge

If you want to schedule another build, you need to add the 🔨 test-with-buildbots label again.