feat: replace Directus with custom Node.js GraphQL backend

Removes Directus 11 and replaces it with a lean, purpose-built backend:
- packages/backend/: Fastify v5 + GraphQL Yoga v5 + Pothos (code-first)
  with Drizzle ORM, Redis sessions (session_token cookie), argon2 auth,
  Nodemailer, fluent-ffmpeg, and full gamification system ported from bundle
- Frontend: @directus/sdk replaced by graphql-request v7; services.ts fully
  rewritten with identical signatures; directus.ts now re-exports from api.ts
- Cookie renamed directus_session_token → session_token
- Dev proxy target updated 8055 → 4000
- compose.yml: Directus service removed, backend service added (port 4000)
- Dockerfile.backend: new multi-stage image with ffmpeg
- Dockerfile: bundle build step and ffmpeg removed from frontend image
- data-migration.ts: one-time script to migrate all Directus/sexy_ tables

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/backend/src/lib/email.ts

@@ -0,0 +1,32 @@
+import nodemailer from "nodemailer";
+
+const transporter = nodemailer.createTransport({
+  host: process.env.SMTP_HOST || "localhost",
+  port: parseInt(process.env.SMTP_PORT || "587"),
+  secure: process.env.SMTP_SECURE === "true",
+  auth: process.env.SMTP_USER ? {
+    user: process.env.SMTP_USER,
+    pass: process.env.SMTP_PASS,
+  } : undefined,
+});
+
+const FROM = process.env.EMAIL_FROM || "noreply@sexy.pivoine.art";
+const BASE_URL = process.env.PUBLIC_URL || "http://localhost:3000";
+
+export async function sendVerification(email: string, token: string): Promise<void> {
+  await transporter.sendMail({
+    from: FROM,
+    to: email,
+    subject: "Verify your email",
+    html: `<p>Click <a href="${BASE_URL}/signup/verify?token=${token}">here</a> to verify your email.</p>`,
+  });
+}
+
+export async function sendPasswordReset(email: string, token: string): Promise<void> {
+  await transporter.sendMail({
+    from: FROM,
+    to: email,
+    subject: "Reset your password",
+    html: `<p>Click <a href="${BASE_URL}/password/reset?token=${token}">here</a> to reset your password.</p>`,
+  });
+}