[8.17](backport #6927) Fix deadlock in error handling in OTelManager

[mergify]

What does this PR do?

Fixes an issue where a deadlock would cause the the OTelManager to get stuck.

This also seems to be the cause of the flaky test TestOTelManager_Run. I have ran this over 100 times and hit no more errors with this PR.

Why is it important?

Deadlock causes the running internal OTel collector from getting any more updates or actions.

Checklist

• I have read and understood the pull request guidelines of this project.
• My code follows the style guidelines of this project
• I have commented my code, particularly in hard-to-understand areas
• [ ] I have made corresponding changes to the documentation
• [ ] I have made corresponding change to the default configuration files
• I have added tests that prove my fix is effective or that my feature works
• I have added an entry in ./changelog/fragments using the changelog tool
• [ ] I have added an integration test or an E2E test

Disruptive User Impact

None

How to test this PR locally

go test -race -v -count=100 github.com/elastic/elastic-agent/internal/pkg/otel/manager

Related issues

• Closes [Flaky Test]: TestOTelManager_Run – otel collector never got healthy #6119

---

This is an automatic backport of pull request #6927 done by [Mergify](https://mergify.com).

[mergify]

Cherry-pick of 9b572ef has failed:

On branch mergify/bp/8.17/pr-6927
Your branch is up to date with 'origin/8.17'.

You are currently cherry-picking commit 9b572efd2.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	new file:   changelog/fragments/1739981369-Fix-deadlock-in-OTelManager.yaml

Unmerged paths:
  (use "git add/rm <file>..." as appropriate to mark resolution)
	deleted by us:   internal/pkg/otel/manager/manager.go
	deleted by us:   internal/pkg/otel/manager/manager_test.go

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

[blakerouse]

Too far back. I didn't know it included this far back in the backports.