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.

backend/scripts/db_backup.sh

@@ -0,0 +1,38 @@
+#!/bin/bash
+# GoChat Database Backup Script
+# Reference: Chatwoot uses pg_dump for backup in production deployments
+# Usage: ./scripts/db_backup.sh [env]
+
+set -euo pipefail
+
+ENV="${1:-production}"
+TIMESTAMP=$(date +%Y%m%d_%H%M%S)
+BACKUP_DIR="${GOCHAT_BACKUP_DIR:-/var/backups/gochat}"
+DB_NAME="${POSTGRES_DB:-gochat_production}"
+DB_USER="${POSTGRES_USER:-gochat}"
+DB_HOST="${POSTGRES_HOST:-localhost}"
+DB_PORT="${POSTGRES_PORT:-5432}"
+RETENTION_DAYS="${GOCHAT_BACKUP_RETENTION_DAYS:-30}"
+
+mkdir -p "${BACKUP_DIR}"
+
+BACKUP_FILE="${BACKUP_DIR}/${DB_NAME}_${TIMESTAMP}.sql.gz"
+
+echo "[$(date)] Starting backup of ${DB_NAME} on ${DB_HOST}:${DB_PORT}"
+
+# pg_dump with compression — mirrors Chatwoot backup approach
+PGPASSWORD="${POSTGRES_PASSWORD}" pg_dump     -h "${DB_HOST}"     -p "${DB_PORT}"     -U "${DB_USER}"     -d "${DB_NAME}"     --format=custom     --compress=9     | gzip > "${BACKUP_FILE}"
+
+BACKUP_SIZE=$(du -h "${BACKUP_FILE}" | cut -f1)
+echo "[$(date)] Backup complete: ${BACKUP_FILE} (${BACKUP_SIZE})"
+
+# Prune old backups beyond retention period
+find "${BACKUP_DIR}" -name "*.sql.gz" -mtime +"${RETENTION_DAYS}" -delete
+echo "[$(date)] Pruned backups older than ${RETENTION_DAYS} days"
+
+# Verify backup integrity
+gunzip -t "${BACKUP_FILE}" && echo "[$(date)] Backup integrity verified" || {
+    echo "[$(date)] ERROR: Backup integrity check failed!"
+    rm -f "${BACKUP_FILE}"
+    exit 1
+}