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/Makefile

@@ -0,0 +1,85 @@
+# GoChat Makefile
+# Reference: Chatwoot Makefile pattern (setup, db, server, docker, run)
+
+APP_NAME := gochat
+GO_ENV ?= development
+
+# Go build flags
+LDFLAGS := -s -w
+BUILD_DIR := ./bin
+
+# Targets
+.PHONY: all setup build run dev test lint clean docker db_create db_migrate db_seed db_reset migrate help
+
+all: build
+
+## setup: Install dependencies
+setup:
+	go mod download
+	go mod tidy
+
+## build: Compile the binary
+build:
+	go build -ldflags "$(LDFLAGS)" -o $(BUILD_DIR)/$(APP_NAME) ./cmd/gochat/
+
+## run: Run the compiled binary
+run: build
+	./$(BUILD_DIR)/$(APP_NAME)
+
+## dev: Run in development mode with hot reload (requires air)
+dev:
+	air -c .air.toml
+
+## test: Run tests
+test:
+	go test -v -race ./...
+
+## test-cover: Run tests with coverage
+test-cover:
+	go test -v -race -coverprofile=coverage.out ./...
+	go tool cover -html=coverage.out -o coverage.html
+
+## lint: Run golangci-lint
+lint:
+	golangci-lint run ./...
+
+## clean: Remove build artifacts
+clean:
+	rm -rf $(BUILD_DIR)
+	rm -f coverage.out coverage.html
+
+## docker: Build Docker image
+docker:
+	docker build -t $(APP_NAME) -f ../deploy/docker/Dockerfile ../
+
+## db_create: Create database (ref: Chatwoot make db_create)
+db_create:
+	@echo "Creating database..."
+	GOCHAT_ENV=$(GO_ENV) ./scripts/migrate.sh create
+
+## db_migrate: Run migrations (ref: Chatwoot make db_migrate)
+db_migrate:
+	@echo "Running migrations..."
+	GOCHAT_ENV=$(GO_ENV) ./scripts/migrate.sh up
+
+## db_seed: Seed data (ref: Chatwoot make db_seed)
+db_seed:
+	@echo "Seeding database..."
+	GOCHAT_ENV=$(GO_ENV) ./scripts/seed.sh
+
+## db_reset: Reset database (ref: Chatwoot make db_reset)
+db_reset:
+	@echo "Resetting database..."
+	GOCHAT_ENV=$(GO_ENV) ./scripts/migrate.sh down
+	GOCHAT_ENV=$(GO_ENV) ./scripts/migrate.sh up
+	GOCHAT_ENV=$(GO_ENV) ./scripts/seed.sh
+
+## migrate: Create a new migration file
+migrate:
+	@read -p "Migration name: " name; 	migrate create -ext sql -dir migrations -seq $$name
+
+## help: Show this help
+help:
+	@echo "GoChat Makefile Commands:"
+	@echo ""
+	@grep -E '^## ' $(MAKEFILE_LIST) | sort | awk 'BEGIN {FS = ": "}; {printf "\033[36m%-20s\033[0m %s\n", $$1, $$2}' | sed 's/## //g'