chore: turn OpenAIMixin into a pydantic.BaseModel (#3671)

# What does this PR do?

- implement get_api_key instead of relying on
LiteLLMOpenAIMixin.get_api_key
 - remove use of LiteLLMOpenAIMixin
 - add default initialize/shutdown methods to OpenAIMixin
 - remove __init__s to allow proper pydantic construction
- remove dead code from vllm adapter and associated / duplicate unit
tests
 - update vllm adapter to use openaimixin for model registration
 - remove ModelRegistryHelper from fireworks & together adapters
 - remove Inference from nvidia adapter
 - complete type hints on embedding_model_metadata
- allow extra fields on OpenAIMixin, for model_store, __provider_id__,
etc
 - new recordings for ollama
 - enhance the list models error handling
- update cerebras (remove cerebras-cloud-sdk) and anthropic (custom
model listing) inference adapters
 - parametrized test_inference_client_caching
- remove cerebras, databricks, fireworks, together from blanket mypy
exclude
 - removed unnecessary litellm deps

## Test Plan

ci

llama_stack/providers/remote/inference/anthropic/anthropic.py

@@ -4,13 +4,19 @@
 # This source code is licensed under the terms described in the LICENSE file in
 # the root directory of this source tree.
 
-from llama_stack.providers.utils.inference.litellm_openai_mixin import LiteLLMOpenAIMixin
+from collections.abc import Iterable
+
+from anthropic import AsyncAnthropic
+
 from llama_stack.providers.utils.inference.openai_mixin import OpenAIMixin
 
 from .config import AnthropicConfig
 
 
-class AnthropicInferenceAdapter(OpenAIMixin, LiteLLMOpenAIMixin):
+class AnthropicInferenceAdapter(OpenAIMixin):
+    config: AnthropicConfig
+
+    provider_data_api_key_field: str = "anthropic_api_key"
     # source: https://docs.claude.com/en/docs/build-with-claude/embeddings
     # TODO: add support for voyageai, which is where these models are hosted
     # embedding_model_metadata = {
@@ -23,22 +29,11 @@ class AnthropicInferenceAdapter(OpenAIMixin, LiteLLMOpenAIMixin):
     #     "voyage-multimodal-3": {"embedding_dimension": 1024, "context_length": 32000},
     # }
 
-    def __init__(self, config: AnthropicConfig) -> None:
-        LiteLLMOpenAIMixin.__init__(
-            self,
-            litellm_provider_name="anthropic",
-            api_key_from_config=config.api_key,
-            provider_data_api_key_field="anthropic_api_key",
-        )
-        self.config = config
-
-    async def initialize(self) -> None:
-        await super().initialize()
-
-    async def shutdown(self) -> None:
-        await super().shutdown()
-
-    get_api_key = LiteLLMOpenAIMixin.get_api_key
+    def get_api_key(self) -> str:
+        return self.config.api_key or ""
 
     def get_base_url(self):
         return "https://api.anthropic.com/v1"
+
+    async def list_provider_model_ids(self) -> Iterable[str]:
+        return [m.id async for m in AsyncAnthropic(api_key=self.get_api_key()).models.list()]