fix(mypy): resolve OpenAI SDK and provider type issues (#3936)

## Summary
- Fix OpenAI SDK NotGiven/Omit type mismatches in embeddings calls
- Fix incorrect OpenAIChatCompletionChunk import in vllm provider
- Refactor to avoid type:ignore comments by using conditional kwargs

## Changes
**openai_mixin.py (9 errors fixed):**
- Build kwargs conditionally for embeddings.create() to avoid
NotGiven/Omit mismatch
- Only include parameters when they have actual values (not None)

**gemini.py (9 errors fixed):**
- Apply same conditional kwargs pattern
- Add missing Any import

**vllm.py (2 errors fixed):**
- Use correct OpenAIChatCompletionChunk from llama_stack.apis.inference
- Remove incorrect alias from openai package

## Technical Notes
The OpenAI SDK has a type system quirk where `NOT_GIVEN` has type
`NotGiven` but parameter signatures expect `Omit`. By only passing
parameters with actual values, we avoid this mismatch entirely without
needing `# type: ignore` comments.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude <noreply@anthropic.com>

src/llama_stack/providers/remote/files/s3/files.py

@@ -4,14 +4,19 @@
 # This source code is licensed under the terms described in the LICENSE file in
 # the root directory of this source tree.
 
+from __future__ import annotations
+
 import uuid
 from datetime import UTC, datetime
-from typing import Annotated, Any
+from typing import TYPE_CHECKING, Annotated, Any, cast
 
 import boto3
 from botocore.exceptions import BotoCoreError, ClientError, NoCredentialsError
 from fastapi import Depends, File, Form, Response, UploadFile
 
+if TYPE_CHECKING:
+    from mypy_boto3_s3.client import S3Client
+
 from llama_stack.apis.common.errors import ResourceNotFoundError
 from llama_stack.apis.common.responses import Order
 from llama_stack.apis.files import (
@@ -34,7 +39,7 @@ from .config import S3FilesImplConfig
 # TODO: provider data for S3 credentials
 
 
-def _create_s3_client(config: S3FilesImplConfig) -> boto3.client:
+def _create_s3_client(config: S3FilesImplConfig) -> S3Client:
     try:
         s3_config = {
             "region_name": config.region,
@@ -52,13 +57,16 @@ def _create_s3_client(config: S3FilesImplConfig) -> boto3.client:
                 }
             )
 
-        return boto3.client("s3", **s3_config)
+        # Both cast and type:ignore are needed here:
+        # - cast tells mypy the return type for downstream usage (S3Client vs generic client)
+        # - type:ignore suppresses the call-overload error from boto3's complex overloaded signatures
+        return cast("S3Client", boto3.client("s3", **s3_config))  # type: ignore[call-overload]
 
     except (BotoCoreError, NoCredentialsError) as e:
         raise RuntimeError(f"Failed to initialize S3 client: {e}") from e
 
 
-async def _create_bucket_if_not_exists(client: boto3.client, config: S3FilesImplConfig) -> None:
+async def _create_bucket_if_not_exists(client: S3Client, config: S3FilesImplConfig) -> None:
     try:
         client.head_bucket(Bucket=config.bucket_name)
     except ClientError as e:
@@ -76,7 +84,7 @@ async def _create_bucket_if_not_exists(client: boto3.client, config: S3FilesImpl
                 else:
                     client.create_bucket(
                         Bucket=config.bucket_name,
-                        CreateBucketConfiguration={"LocationConstraint": config.region},
+                        CreateBucketConfiguration=cast(Any, {"LocationConstraint": config.region}),
                     )
             except ClientError as create_error:
                 raise RuntimeError(
@@ -128,7 +136,7 @@ class S3FilesImpl(Files):
     def __init__(self, config: S3FilesImplConfig, policy: list[AccessRule]) -> None:
         self._config = config
         self.policy = policy
-        self._client: boto3.client | None = None
+        self._client: S3Client | None = None
         self._sql_store: AuthorizedSqlStore | None = None
 
     def _now(self) -> int:
@@ -184,7 +192,7 @@ class S3FilesImpl(Files):
         pass
 
     @property
-    def client(self) -> boto3.client:
+    def client(self) -> S3Client:
         assert self._client is not None, "Provider not initialized"
         return self._client