feat: migrate Inspect API to FastAPI router (#4403)

# What does this PR do?

Migrate the Inspect API to the FastAPI router pattern.

Changes:
- Add inspect API to FastAPI router registry
- Add PUBLIC_ROUTE_KEY support for routes that don't require auth
- Update WebMethod creation to respect route's openapi_extra for
authentication requirements

Fixes: https://github.com/llamastack/llama-stack/issues/4346

<!-- Provide a short summary of what this PR does and why. Link to
relevant issues if applicable. -->

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## Test Plan

CI and various curls on /v1/inspect/routes, /v1/health, /v1/version

Signed-off-by: Sébastien Han <seb@redhat.com>

src/llama_stack_api/inspect_api/models.py

@@ -0,0 +1,53 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the terms described in the LICENSE file in
+# the root directory of this source tree.
+
+"""Pydantic models for Inspect API requests and responses.
+
+This module defines the request and response models for the Inspect API
+using Pydantic with Field descriptions for OpenAPI schema generation.
+"""
+
+from typing import Literal
+
+from pydantic import BaseModel, Field
+
+from llama_stack_api.datatypes import HealthStatus
+from llama_stack_api.schema_utils import json_schema_type
+
+# Valid values for the route filter parameter.
+# Actual API levels: v1, v1alpha, v1beta (filters by level, excludes deprecated)
+# Special filter value: "deprecated" (shows deprecated routes regardless of level)
+ApiFilter = Literal["v1", "v1alpha", "v1beta", "deprecated"]
+
+
+@json_schema_type
+class RouteInfo(BaseModel):
+    """Information about an API route including its path, method, and implementing providers."""
+
+    route: str = Field(description="The API route path")
+    method: str = Field(description="The HTTP method for the route")
+    provider_types: list[str] = Field(description="List of provider types implementing this route")
+
+
+@json_schema_type
+class HealthInfo(BaseModel):
+    """Health status information for the service."""
+
+    status: HealthStatus = Field(description="The health status of the service")
+
+
+@json_schema_type
+class VersionInfo(BaseModel):
+    """Version information for the service."""
+
+    version: str = Field(description="The version string of the service")
+
+
+@json_schema_type
+class ListRoutesResponse(BaseModel):
+    """Response containing a list of all available API routes."""
+
+    data: list[RouteInfo] = Field(description="List of available API routes")