Add method for updating custom_scheduling last_synced

[navarone-feekery]

Related to https://github.com/elastic/enterprise-search-team/issues/3594

Add method to update custom_scheduling.[key].last_synced value with current time.

Checklists

Pre-Review Checklist

• [x] Covered the changes with automated tests
• [x] Tested the changes locally
• [x] Added a label for each target release version (example: v7.13.2, v7.14.0, v8.0.0)