Add OpenAPI spec generation via utoipa with /openapi.json endpoint

Integrate utoipa 5 to auto-generate an OpenAPI 3.1 spec from the existing
Axum handlers and serde types. All 16 endpoints are annotated with path
metadata, request/response schemas, security requirements, and tags. A
public /openapi.json endpoint serves the spec without requiring auth.

Includes 59 tests covering path completeness, HTTP methods, schema fields,
enum variants, security scheme, path/query parameters, request bodies,
response references, and endpoint integration.

https://claude.ai/code/session_01NfoPVx21rZUQned1f7WpXY

Cargo.lock

@@ -4603,6 +4603,7 @@ dependencies = [
  "tower-http",
  "tracing",
  "tracing-subscriber",
+ "utoipa",
 ]
 
 [[package]]
@@ -6924,6 +6925,30 @@ version = "0.2.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "06abde3611657adf66d383f00b093d7faecc7fa57071cce2578660c9f1010821"
 
+[[package]]
+name = "utoipa"
+version = "5.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "2fcc29c80c21c31608227e0912b2d7fddba57ad76b606890627ba8ee7964e993"
+dependencies = [
+ "indexmap 2.13.0",
+ "serde",
+ "serde_json",
+ "utoipa-gen",
+]
+
+[[package]]
+name = "utoipa-gen"
+version = "5.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "6d79d08d92ab8af4c5e8a6da20c47ae3f61a0f1dabc1997cdf2d082b757ca08b"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "regex",
+ "syn 2.0.115",
+]
+
 [[package]]
 name = "uuid"
 version = "1.22.0"