db_model: false on a route created via /model/new

A route created through `/model/new` with `STORE_MODEL_IN_DB=True` comes back
with `model_info.db_model: false`, despite being persisted — it survives and
appears in `/model/info` alongside the YAML-seeded models.

So the flag does not mean what its name suggests, or it is set on the read path
rather than reflecting storage.

Harmless today. Worth pinning down before anything is built that trusts it to
distinguish DB-backed routes from YAML-seeded ones — which is exactly the
distinction "Move fleet state into LiteLLM" and "Surface config skew on the /fleet page" care about, since skew detection needs to know which
routes llmao owns and which came from the seed.

Cheap check: restart the proxy and see whether the flag or the route changes.

Reproduce the behavior through /model/new with STORE_MODEL_IN_DB=True, then restart the proxy and inspect the result in /model/info. Compare the db_model flag and route persistence before and after restart; done means the flag accurately distinguishes DB-backed routes from YAML-seeded models.

Written by the indexing model from the issue text.