[PTFOPlayer]

OpenAI-compatible gateways and llama.cpp-style servers frequently ship without a /health route, so the startup check failed with a bare "404 (no /health endpoint)" warning even when the backend was perfectly usable — leaving --skip-health-check as the only way to silence it.

health_check() now treats an HTTP 404 on /health as "endpoint missing" rather than "server unhealthy" and probes /v1/models instead: a non-empty model list proves the backend is reachable and serving, so it counts as a successful check. An empty list or a failing model request still reports an error naming both endpoints. Other /health statuses (5xx, 401, transport failures) are surfaced unchanged — the fallback never masks an endpoint that exists but is unhappy.

• add fetch_models_raw(): strict variant that separates "answered with an empty list" from "request could not complete", which the health check needs to interpret the result. fetch_model_list() becomes a thin wrapper, keeping its lenient contract so model auto-selection is untouched
• add models_url(), normalising a trailing /v1 the same way chat_url() does
• cover all six paths with unit tests against a minimal in-test HTTP mock (tokio TcpListener, no new dependencies)
• document the fallback in the Provider trait, the skip_health_check setting, the --skip-health-check help, README and TINYHARNESS.md

Ollama needs no change (its health check already is a model listing) and Sockudo is left alone: its /up/ route reports tunnel status, not OpenAI compatibility.