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/backend/prisma/migrations/20260529183748_add_auth/migration.sql

@@ -0,0 +1,78 @@
+-- CreateTable
+CREATE TABLE "user" (
+    "id" TEXT NOT NULL,
+    "name" TEXT NOT NULL,
+    "email" TEXT NOT NULL,
+    "emailVerified" BOOLEAN NOT NULL DEFAULT false,
+    "image" TEXT,
+    "createdAt" TIMESTAMP(3) NOT NULL DEFAULT CURRENT_TIMESTAMP,
+    "updatedAt" TIMESTAMP(3) NOT NULL,
+
+    CONSTRAINT "user_pkey" PRIMARY KEY ("id")
+);
+
+-- CreateTable
+CREATE TABLE "session" (
+    "id" TEXT NOT NULL,
+    "expiresAt" TIMESTAMP(3) NOT NULL,
+    "token" TEXT NOT NULL,
+    "createdAt" TIMESTAMP(3) NOT NULL DEFAULT CURRENT_TIMESTAMP,
+    "updatedAt" TIMESTAMP(3) NOT NULL,
+    "ipAddress" TEXT,
+    "userAgent" TEXT,
+    "userId" TEXT NOT NULL,
+
+    CONSTRAINT "session_pkey" PRIMARY KEY ("id")
+);
+
+-- CreateTable
+CREATE TABLE "account" (
+    "id" TEXT NOT NULL,
+    "accountId" TEXT NOT NULL,
+    "providerId" TEXT NOT NULL,
+    "userId" TEXT NOT NULL,
+    "accessToken" TEXT,
+    "refreshToken" TEXT,
+    "idToken" TEXT,
+    "accessTokenExpiresAt" TIMESTAMP(3),
+    "refreshTokenExpiresAt" TIMESTAMP(3),
+    "scope" TEXT,
+    "password" TEXT,
+    "createdAt" TIMESTAMP(3) NOT NULL DEFAULT CURRENT_TIMESTAMP,
+    "updatedAt" TIMESTAMP(3) NOT NULL,
+
+    CONSTRAINT "account_pkey" PRIMARY KEY ("id")
+);
+
+-- CreateTable
+CREATE TABLE "verification" (
+    "id" TEXT NOT NULL,
+    "identifier" TEXT NOT NULL,
+    "value" TEXT NOT NULL,
+    "expiresAt" TIMESTAMP(3) NOT NULL,
+    "createdAt" TIMESTAMP(3) NOT NULL DEFAULT CURRENT_TIMESTAMP,
+    "updatedAt" TIMESTAMP(3) NOT NULL,
+
+    CONSTRAINT "verification_pkey" PRIMARY KEY ("id")
+);
+
+-- CreateIndex
+CREATE UNIQUE INDEX "user_email_key" ON "user"("email");
+
+-- CreateIndex
+CREATE UNIQUE INDEX "session_token_key" ON "session"("token");
+
+-- CreateIndex
+CREATE INDEX "session_userId_idx" ON "session"("userId");
+
+-- CreateIndex
+CREATE INDEX "account_userId_idx" ON "account"("userId");
+
+-- CreateIndex
+CREATE INDEX "verification_identifier_idx" ON "verification"("identifier");
+
+-- AddForeignKey
+ALTER TABLE "session" ADD CONSTRAINT "session_userId_fkey" FOREIGN KEY ("userId") REFERENCES "user"("id") ON DELETE CASCADE ON UPDATE CASCADE;
+
+-- AddForeignKey
+ALTER TABLE "account" ADD CONSTRAINT "account_userId_fkey" FOREIGN KEY ("userId") REFERENCES "user"("id") ON DELETE CASCADE ON UPDATE CASCADE;