list_authenticated_providers() was using env var names from the external
models.dev registry to detect credentials. This registry has incorrect
mappings for 5 providers: minimax-cn, zai, opencode-zen, opencode-go,
and kilocode — causing them to not appear in /model even when the
correct API key is set.
Now checks PROVIDER_REGISTRY from auth.py first (our source of truth),
falling back to models.dev only for providers not in our registry.
Fixes#6620. Based on devorun's investigation in PR #6625.