### What happened?

DB-stored auto-router / complexity-router models (`litellm_params.model = "auto_router/..."`) permanently disappear from `/v1/models`, `/model/info`, and `/model_group/info` — even for the master key — while continuing to serve completions. Once delisted they cannot be re-listed without deleting the row AND restarting the proxy.

Verified lifecycle on a live proxy (1.92.0, `STORE_MODEL_IN_DB=true`), reproducible at will:

1. `POST /model/new` with a `complexity_router_config` row → listed, routes, and **stable** across the 30s DB sync cycles. ✅ 2. `PATCH /model/{id}/update` on that row → **instantly and permanently delisted**, and the patched config is silently ignored (the stale in-memory router keeps serving the OLD tiers). ❌ 3. `POST /model/delete` → removed from DB/listing but **keeps routing as a ghost** until restart. ❌ 4. Any replica restart → rows load at startup, then get delisted within one sync cycle. ❌

Downstream impact: clients that build their model list from `/models` (LibreChat `fetch: true`, OpenWebUI, etc.) can never see or validate the auto-router model names.

### Root cause

Every deployment-removal path cleans `self.model_list` but never t…