[Enhancement] Resolve Various Hanging Issues During Init Process

[pi314ever]

PLEASE FILL IN THE PR DESCRIPTION HERE ENSURING ALL CHECKLIST ITEMS (AT THE BOTTOM) HAVE BEEN CONSIDERED.

Purpose

Resolves various issues that lead to processes hanging or timeout mentioned in #1346. Namely:

• Raise TimeoutError on stage initialization timeout to prevent invalid orchestrator state (ready with one or more stages timed out)
• Exit early from test OmniServer if server process is dead
• Resolve hanging issues in OmniStage.try_collect() by checking for dead proccesses

Test Plan

Test Result

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[xuechendi]

@hsliuustc0106 , when one initialization stage failed due timeout, why we want to keep it running instead of terminate?
Is it OK to switch to terminate?

[pi314ever]

I split this into 4 pull requests due to potential discussions required around each integration. This issue will be closed in favor of them:

• [Enhancement] Escalate stage timeout to error #1558 for escalating stage timeouts to actual errors
• [Enhancement][pytest] Check for process running during start server #1559 to fix pytest timeouts
• [Enhancement] Patch OmniStage.try_collect() with _proc alive checks #1560 and [Enhancement] Patch OmniStage.try_collect() with ray alive checks #1561 to fix OmniStage.try_collect() validation for mp.Process and ray, respectively.