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/cmd/dump_routes/main.go

@@ -0,0 +1,60 @@
+package main
+
+import (
+	"fmt"
+	"os"
+	"sort"
+	"strings"
+
+	"github.com/gin-gonic/gin"
+	"github.com/gochat/gochat/internal/config"
+	v1 "github.com/gochat/gochat/internal/handler/api/v1"
+	"github.com/gochat/gochat/internal/middleware"
+	"github.com/gochat/gochat/internal/router"
+)
+
+func main() {
+	gin.SetMode(gin.TestMode)
+	engine := gin.New()
+
+	cfg, err := config.Load()
+	if err != nil {
+		fmt.Fprintf(os.Stderr, "config load: %v\n", err)
+		os.Exit(1)
+	}
+
+	// Create mostly zero-value handlers — we only need route paths, not working handlers.
+	handlers := &router.Handlers{EnterpriseAccount: v1.NewEnterpriseAccountHandler(nil)}
+
+	corsCfg := middleware.CORSConfigFromAppConfig(cfg)
+	router.RegisterRoutes(
+		engine,
+		nil, // jwtService
+		nil, // refreshStore
+		nil, // webhookRegistry
+		handlers,
+		nil, // hub
+		nil, // wsAuthenticator
+		&cfg.JWT,
+		corsCfg,
+		nil, // db
+	)
+
+	routes := engine.Routes()
+	sort.Slice(routes, func(i, j int) bool {
+		if routes[i].Method != routes[j].Method {
+			return routes[i].Method < routes[j].Method
+		}
+		return routes[i].Path < routes[j].Path
+	})
+
+	count := 0
+	for _, r := range routes {
+		if strings.HasPrefix(r.Path, "/swagger") {
+			continue
+		}
+		fmt.Printf("%s %s\n", r.Method, r.Path)
+		count++
+	}
+	fmt.Printf("TOTAL: %d\n", count)
+}