Add a ``readiness_probe`` constructor kwarg accepting "models",
"chat_completions", or "both", and flip the default from the older
catalog-only ``GET /v1/models`` probe to a new ``POST /v1/chat/
completions`` probe with ``max_tokens=1``.

Motivation: OpenAI-compatible proxies can return 200 on the catalog
endpoint while rejecting completions (Bifrost is the field-reported
case), so the previous probe reported ready while every real call
failed. The new default actually exercises the inference wire path,
so that failure class surfaces at preflight. Non-200 chat-probe
responses route through ``classify_http_error`` so canonical error
categories surface consistently. Catalog-only behavior remains opt-in
for cost-sensitive cloud callers.

Conformance harness picks ``readiness_probe`` mode from the fixture's
mocked ``health_endpoint.path`` so fixture 007's catalog semantics
keep working without spec changes.

Three findings on PR #109:

1. Runtime guard for ``readiness_probe``. The Literal type is a static
   hint; an unknown string would silently no-op both dispatch branches
   in ``ready()`` and report ready. Validate in ``__init__`` against a
   module-level frozenset and raise ValueError.
2. Route ``_probe_models`` non-200 responses through
   ``classify_http_error``. Previously hard-coded 401/403 to
   ProviderAuthentication and everything-else to ProviderUnavailable,
   missing ProviderRateLimit (429), ProviderModelNotLoaded (503+marker),
   and ProviderInvalidModel (404+marker). The docstring's
   mode-independence claim is now true.
3. Validate ``_probe_chat_completions`` 200 response shape. A proxy
   answering 200 with an error payload or non-OpenAI-shape JSON
   previously passed the probe. Mirror ``_do_complete``'s parse +
   ``_parse_response(payload, None, None)`` step.

Adds five new tests covering: invalid mode at construction, catalog
probe 429 → ProviderRateLimit, catalog probe 503+marker →
ProviderModelNotLoaded, chat probe 200 with error payload, and chat
probe 200 with non-JSON body.