feat: migrate authentication to Better-Auth (Phase 1)

Replace hand-rolled JWT auth with Better-Auth session-based authentication.

- Scaffold auth/ Node.js service with Better-Auth, bcrypt password compat,
  Postgres adapter mapped to existing users table
- Add Alembic migration (002) creating sessions, accounts, verifications
  tables and migrating password hashes to accounts table
- Update FastAPI auth dependency to validate sessions via shared DB
  (supports both cookie and Bearer token)
- Remove registration/login/refresh endpoints from API gateway (now
  handled by Better-Auth service)
- Update frontend to use better-auth/react client with httpOnly cookies
  (no tokens in localStorage or memory)
- Rewrite auth store, Login, Register, Dashboard, Settings, ProtectedRoute
  to use session-based auth
- Update all tests to create sessions directly in DB instead of JWT tokens

Resolves CAR-27
See plan: CAR-26#document-plan

Co-Authored-By: Paperclip <noreply@paperclip.ing>

tests/test_e2e/conftest.py

@@ -10,9 +10,9 @@ from decimal import Decimal
 from uuid import UUID
 
 import pytest
+from sqlalchemy import text
 from sqlalchemy.ext.asyncio import AsyncSession, async_sessionmaker
 
-from cartsnitch_api.auth.jwt import decode_token
 from cartsnitch_api.models import (
     Coupon,
     NormalizedProduct,
@@ -126,10 +126,16 @@ async def seed_data(db_engine, auth_headers):
         session.add_all(prices)
         await session.flush()
 
-        # -- Purchases (need the user_id from the registered test user) --
-        token = auth_headers["Authorization"].split(" ")[1]
-        payload = decode_token(token)
-        user_id = UUID(payload["sub"])
+        # -- Get the user_id from the session token in auth_headers --
+        cookie_str = auth_headers.get("Cookie", "")
+        session_token = cookie_str.split("=", 1)[1] if "=" in cookie_str else ""
+
+        result = await session.execute(
+            text("SELECT user_id FROM sessions WHERE token = :token"),
+            {"token": session_token},
+        )
+        row = result.first()
+        user_id = UUID(row[0])
 
         purchase1 = Purchase(
             user_id=user_id,