Reorganize repo: backend/, deploy/, docs/ layout + AGENTS.md

Restructure the monorepo into clear top-level directories:
- backend/: Go module root (cmd, internal, pkg, configs, migrations,
  docs/swagger, scripts, tests, go.mod, Makefile, .air.toml)
- deploy/: Docker (Dockerfile, docker-compose*), quickstart, fluentd
- docs/: project documentation + reports/ (moved from repo root)
- AGENTS.md: new AI coding-agent guide at repo root

Update all references to the new layout:
- Dockerfile: COPY backend/go.mod, COPY backend/ (context = repo root)
- docker-compose files: context ../.., dockerfile deploy/docker/Dockerfile,
  env_file ../../.env, volume mounts ../../backend:/app
- deploy/quickstart/compose.yaml: dockerfile deploy/docker/Dockerfile
- CI: working-directory: backend for go commands, file deploy/docker/Dockerfile,
  coverage path backend/coverage.out, health_check backend/scripts/
- backend/Makefile: docker target uses -f ../deploy/docker/Dockerfile ../
- README: architecture tree, quickstart, config paths updated

Move root stray scripts (rename_models.*, run_m11_tests.sh, verify_build.sh,
gorm_bool_main.go) to backend/scripts/legacy/. All moves via git mv to
preserve history. Build, vet, SQLite tests, and docker compose config verified.

deploy/docker/docker-compose.yml

@@ -0,0 +1,72 @@
+# GoChat Development Environment
+# Reference: Chatwoot docker-compose.yaml development setup
+# Provides PostgreSQL + Redis + Mailhog for local development
+
+version: '3.8'
+
+services:
+  postgres:
+    image: postgres:16-alpine
+    container_name: gochat-postgres
+    environment:
+      POSTGRES_DB: gochat_dev
+      POSTGRES_USER: postgres
+      POSTGRES_PASSWORD: postgres
+    ports:
+      - "5432:5432"
+    volumes:
+      - postgres_data:/var/lib/postgresql/data
+    healthcheck:
+      test: ["CMD-SHELL", "pg_isready -U postgres"]
+      interval: 5s
+      timeout: 5s
+      retries: 5
+
+  redis:
+    image: redis:7-alpine
+    container_name: gochat-redis
+    ports:
+      - "6379:6379"
+    volumes:
+      - redis_data:/data
+    healthcheck:
+      test: ["CMD", "redis-cli", "ping"]
+      interval: 5s
+      timeout: 5s
+      retries: 5
+
+  mailhog:
+    image: mailhog/mailhog:v1.0.1
+    container_name: gochat-mailhog
+    ports:
+      - "1025:1025"   # SMTP
+      - "8025:8025"   # Web UI
+    # Reference: Chatwoot docker-compose includes mailhog for email testing
+
+  gochat:
+    build:
+      context: ../..
+      dockerfile: deploy/docker/Dockerfile
+    container_name: gochat-app
+    depends_on:
+      postgres:
+        condition: service_healthy
+      redis:
+        condition: service_healthy
+    ports:
+      - "3000:3000"
+    env_file: ../../.env
+    environment:
+      - GOCHAT_ENV=development
+      - POSTGRES_HOST=postgres
+      - POSTGRES_PORT=5432
+      - POSTGRES_DATABASE=gochat_dev
+      - POSTGRES_USERNAME=postgres
+      - POSTGRES_PASSWORD=postgres
+      - REDIS_URL=redis://redis:6379
+    volumes:
+      - ../../backend:/app:delegated
+
+volumes:
+  postgres_data:
+  redis_data: