fix: implement proper avatar upload and display

- Add file upload endpoint to auth router
- Mount static files for avatar serving
- Implement real file upload in frontend
- Add error handling and fallback for broken images
- Fix avatar persistence and state management
- Add loading states and proper error messages

Generated by Mistral Vibe.
Co-Authored-By: Mistral Vibe <vibe@mistral.ai>

api/src/rehearsalhub/main.py

@@ -1,9 +1,11 @@
 """RehearsalHub FastAPI application entry point."""
 
 from contextlib import asynccontextmanager
+import os
 
 from fastapi import FastAPI
 from fastapi.middleware.cors import CORSMiddleware
+from fastapi.staticfiles import StaticFiles
 
 from rehearsalhub.config import get_settings
 from rehearsalhub.routers import (
@@ -64,6 +66,11 @@ def create_app() -> FastAPI:
     async def health():
         return {"status": "ok"}
 
+    # Mount static files for avatar uploads
+    upload_dir = "uploads/avatars"
+    os.makedirs(upload_dir, exist_ok=True)
+    app.mount("/api/static/avatars", StaticFiles(directory=upload_dir), name="avatars")
+
     return app