<!-- Add the related story/sub-task/bug number, like Resolves#123, or
remove if NA -->
**Related issue:** Resolves#39228
Manually tested by triggering a failover on loadtest.
# Checklist for submitter
If some of the following don't apply, delete the relevant line.
- [x] Changes file added for user-visible changes in `changes/`,
`orbit/changes/` or `ee/fleetd-chrome/changes`.
## Testing
- [x] Added/updated automated tests
- [x] QA'd all new/changed functionality manually
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
* **Bug Fixes**
* Health checks now detect a primary DB becoming read-only and report
failure so the service restarts and reconnects to a writable primary.
* Write failures due to DB read-only state now trigger immediate fatal
handling to prompt graceful shutdown and recovery.
* Improved detection and handling of read-only DB conditions to increase
stability during failovers.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
