### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

**Expected:** When `background_health_checks` and `use_shared_health_check` are enabled, the public `model_hub_table` (`/ui/model_hub`) should display the same runtime health status shown in the Admin UI Dashboard (i.e. the Redis-backed background health check cache). If a model endpoint is actually failing, the public hub should show `unhealthy`.

**Actual:** The public `model_hub_table` displays a static/config-backed health status that does not reflect the background health check results. For the same failing model, the Admin UI correctly shows `unhealthy` (via `/health/shared-status`), while the public hub continues to show `healthy` or `unknown` sourced from `litellm_modeltable` / static config metadata.

**Configuration context:** ```yaml general_settings: background_health_checks: true use_shared_health_check: true health_check_interval: 3600 ```

This was nominally addressed in #19034, but the implementation appears to read health from the wrong data layer.

### Steps to Reproduce

1. Configure a model with a deliberately broken/…