feat: add email/password auth backend + forgot/reset password routes

- Configure Better Auth emailAndPassword plugin with Resend
- Add email verification and password reset email sending
- Create forgot-password and reset-password frontend routes
- Add auth schemas to @lila/shared

packages/shared/src/index.ts

@@ -1,3 +1,4 @@
 export * from "./constants.js";
 export * from "./schemas/game.js";
 export * from "./schemas/lobby.js";
+export * from "./schemas/auth.js";

packages/shared/src/schemas/auth.ts

@@ -0,0 +1,7 @@
+import * as z from "zod";
+
+export const ResetPasswordSearchSchema = z.object({
+  token: z.string().catch(""),
+});
+
+export type ResetPasswordSearch = z.infer<typeof ResetPasswordSearchSchema>;