feat(auth): implement better authentication system with user sessions and password management

- Added user, session, account, and verification models to Prisma schema.
- Integrated better-auth for user authentication with email and password.
- Created auth middleware for session validation.
- Implemented auth context and client in frontend for managing user sessions.
- Added login and settings pages for user authentication and password management.
- Updated routes to include authentication checks and user-specific content.
- Enhanced UI components to reflect authentication state.

apps/frontend/src/router.tsx

@@ -1,7 +1,21 @@
 import { createRouter } from "@tanstack/react-router";
 import { routeTree } from "./routeTree.gen";
 
-const router = createRouter({ routeTree });
+export interface RouterContext {
+  auth: {
+    session: object | null;
+    isPending: boolean;
+    isAuthenticated: boolean;
+    signIn: (password: string) => Promise<void>;
+    signOut: () => Promise<void>;
+    changePassword: (currentPassword: string, newPassword: string) => Promise<void>;
+  };
+}
+
+const router = createRouter({
+  routeTree,
+  context: {} as RouterContext,
+});
 
 declare module "@tanstack/react-router" {
   interface Register {