feat(api): add configurable CORS middleware

The web UI is multi-instance and can connect to the backend at a
different origin (the direct :8000 port, a LAN IP, 127.0.0.1 vs
localhost), which the browser blocks without CORS headers. Adds
CORSMiddleware driven by a new cors_allow_origins setting (default "*",
safe here: bearer-token auth with allow_credentials=False). Accepts a
comma-separated string in .env.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

app/main.py

@@ -4,6 +4,7 @@ from collections.abc import AsyncIterator
 from contextlib import asynccontextmanager
 
 from fastapi import FastAPI, WebSocket
+from fastapi.middleware.cors import CORSMiddleware
 
 from app.api.errors import register_exception_handlers
 from app.api.health import router as health_router
@@ -40,6 +41,19 @@ def create_app() -> FastAPI:
     )
 
     app.add_middleware(CorrelationIdMiddleware)
+    # CORS added last → outermost, so browser preflight (OPTIONS) is answered
+    # before anything else. The web UI can connect cross-origin (direct :8000,
+    # a LAN IP, 127.0.0.1 vs localhost), which needs these headers. Bearer-token
+    # auth (no cookies) → wildcard origins are safe with allow_credentials=False.
+    if settings.cors_allow_origins:
+        app.add_middleware(
+            CORSMiddleware,
+            allow_origins=settings.cors_allow_origins,
+            allow_credentials=False,
+            allow_methods=["*"],
+            allow_headers=["*"],
+            expose_headers=["Content-Range", "Accept-Ranges", "Content-Length"],
+        )
     register_exception_handlers(app)
 
     app.include_router(health_router)