Flaky test: FunctionsSyncServiceTests: Increase test due time & add tsc callback

[liliankasem]

Issue describing the changes in this PR

Part of #10135

Pull request checklist

IMPORTANT: Currently, changes must be backported to the in-proc branch to be included in Core Tools and non-Flex deployments.

• Backporting to the in-proc branch is not required
  • Otherwise: Link to backporting PR
• 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
  • Otherwise: Backport tracked by issue/PR #issue_or_pr
• 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

Increasing the test due time to something more reasonable

[jviau]

Is there a way we can use mock callbacks to signal the expected method was called? This way we can increase the timeout significantly, but also end delaying once it is called. See #10128 for an example

[liliankasem]

Is there a way we can use mock callbacks to signal the expected method was called? This way we can increase the timeout significantly, but also end delaying once it is called. See #10128 for an example

Will take a stab at this approach