[Alerting] Alerting now uses Task Manager intervals internally

[gmmorris]

Summary

NOTE: No need to review this before we merge in #50718 as it'll make reviewing harder.

Remove the custom implementation of intervals in Alerting to use the Task Manager interval feature.

Resolves #46001

Checklist

Use strikethroughs to remove checklist items you don't feel are applicable to this PR.

• This was checked for cross-browser compatibility, including a check against IE11
• Any text added follows EUI's writing guidelines, uses sentence case text and includes i18n support
• Documentation was added for features that require explanation or tutorials
• Unit or functional tests were updated or added to match the most common scenarios
• This was checked for keyboard-only and screenreader accessibility

For maintainers

• This was checked for breaking API changes and was labeled appropriately
• This includes a feature addition or change that requires a release note and was labeled appropriately

[elasticmachine]

Pinging @elastic/kibana-stack-services (Team:Stack Services)

[elasticmachine]

💚 Build Succeeded

• continuous-integration/kibana-ci/pull-request
• Commit: bae03a4

[elasticmachine]

💚 Build Succeeded

• continuous-integration/kibana-ci/pull-request
• Commit: 0170202

[gmmorris]

@elasticmachine merge upstream

[elasticmachine]

💔 Build Failed

• continuous-integration/kibana-ci/pull-request
• Commit: e0690c4

[gmmorris]

No longer relevant - we'll achieve a similar ability using the upcoming runNow api instead