## Summary
- Index `embeddedPostgresMaxConnections` in Settings search
(backups-global).
- Export `withProjectId` + `api` from `CommandCenterControls` legacy
mock so FN-8284 portability card can mount under the controls suite.
## Test plan
- [x] CommandCenterControls + settings-search-index tests green locally
- [ ] Full Suite all 4 shards green on main after merge
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
* **New Features**
* Added the embedded PostgreSQL maximum connections setting to Settings
search, with relevant labels, help text, and keywords.
* **Tests**
* Improved test coverage setup for controls that use project-specific
API paths.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
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