Start metrics listener after specialization

[liliankasem]

Issue describing the changes in this PR

A bug was found where it appears that metrics are being captured pre-specialization and being persisted, leading to an inflated started invocation count e.g:

'AppFailureCount':0,'ActiveInvocationCount':0,'StartedInvocationCount':123

With this change, we are waiting for specialization to happen before we collect metrics.

Design choices and questions

I am currently utilizing the metrics publisher which lives in Script.WebHost and has access to IOptionsMonitor<StandbyOptions> to listen for OnStandbyOptionsChange. StandbyOptions cannot be imported into the Script project where the HostMetricsProvider lives, so I am open to better suggestions on when to start the listener.

Q: Is starting the listener after specialization enough to fix this issue or do we need to also reset the actual metric for started invocation count?

I am deploying these changes to test them out on a legion stamp.

Pull request checklist

• [ ] My changes do not require documentation changes
  • [ ] Otherwise: Documentation issue linked to PR
• [ ] My changes should not be added to the release notes for the next release
  • [ ] Otherwise: I've added my notes to release_notes.md
• [ ] My changes do not need to be backported to a previous version
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• [ ] My changes do not require diagnostic events changes
  • Otherwise: I have added/updated all related diagnostic events and their documentation (Documentation issue linked to PR)
• [ ] I have added all required tests (Unit tests, E2E tests)

Additional information

Additional PR information