refactor: migrate authentication from Supabase to Better Auth and update Prisma schema models

apps/backend/src/lib/auth.ts

@@ -0,0 +1,27 @@
+import { betterAuth } from "better-auth";
+import { prismaAdapter } from "better-auth/adapters/prisma";
+// If your Prisma file is located elsewhere, you can change the path
+import { openAPI } from "better-auth/plugins";
+import { db } from "./prisma";
+
+export const auth = betterAuth({
+    database: prismaAdapter(db, {
+        provider: "postgresql",
+    }),
+    secret: process.env.BETTER_AUTH_SECRET,
+    baseURL: process.env.BETTER_AUTH_URL,
+    session: {
+        cookieCache: {
+            enabled: false,
+        },
+    },
+    emailAndPassword: {
+        enabled: true,
+    },
+    trustedOrigins: [process.env.APP_BASE_URL ?? "http://localhost:5173"],
+    plugins: [
+    ],
+});
+
+export type Session = typeof auth.$Infer.Session.session;
+export type User = typeof auth.$Infer.Session.user;