Problem

When multiple custom_providers share the same base_url, get_custom_provider_pool_key(base_url) always returns the pool key for the first matching entry. Any other provider at that URL gets the wrong credentials. This is P1 — silently uses the wrong API key.

# Before — always matches provider-a even when provider-b is active
def get_custom_provider_pool_key(base_url: str) -> Optional[str]:
    for norm_name, entry in _iter_custom_providers():
        if entry_url == normalized_url:
            return f"custom:{norm_name}"  # ← first match wins

Fix

Add an optional provider_name parameter. When provided, name-first lookup resolves the correct entry regardless of shared URLs:

def get_custom_provider_pool_key(
    base_url: str, provider_name: Optional[str] = None
) -> Optional[str]:
    # Fast path: match by name when the caller knows which provider is active.
    if provider_name:
        normalized_name = _normalize_custom_pool_name(provider_name)
        for norm_name, entry in _iter_custom_providers():
            if norm_name == normalized_name:
                return f"custom:{norm_name}"
        # Fall through to URL matching as best-effort fallback
    ...

Call site in seed_custom_provider_pool updated to pass model.name as the hint.

Backward compat: All existing callers that only pass base_url get the original first-match behaviour — no change for single-provider setups.

Tests

test_get_custom_provider_pool_key_disambiguates_shared_base_url covers:

• Two providers at the same URL each resolve to their own pool key with name hint
• Name matching is case/whitespace insensitive
• Unknown name falls back to URL match
• Name-only lookup works when base_url is empty

All existing test_get_custom_provider_pool_key assertions still pass.

Fixes #19083