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/internal/handler/metrics_handler.go

@@ -0,0 +1,82 @@
+package handler
+
+import (
+	"fmt"
+	"net/http"
+	"runtime"
+	"time"
+
+	"github.com/gin-gonic/gin"
+)
+
+// MetricsHandler exposes Prometheus-compatible metrics in text exposition format.
+// Reference: Chatwoot uses Prometheus exporter for Sidekiq, Rails metrics
+// This provides Go runtime + application metrics on a dedicated port.
+
+// PrometheusHandler returns metrics in Prometheus text format.
+func PrometheusHandler(startTime time.Time) gin.HandlerFunc {
+	return func(c *gin.Context) {
+		var m runtime.MemStats
+		runtime.ReadMemStats(&m)
+
+		uptime := time.Since(startTime).Seconds()
+
+		metrics := []string{
+			// Go runtime metrics
+			formatGauge("gochat_go_goroutines", uint64(runtime.NumGoroutine())),
+			formatGauge("gochat_go_memory_alloc_bytes", m.Alloc),
+			formatGauge("gochat_go_memory_sys_bytes", m.Sys),
+			formatGauge("gochat_go_memory_total_alloc_bytes", m.TotalAlloc),
+			formatGauge("gochat_go_gc_pause_total_ns", m.PauseTotalNs),
+			formatCounter("gochat_go_gc_count", uint64(m.NumGC)),
+			// Application metrics
+			formatGauge("gochat_uptime_seconds", uint64(uptime)),
+			formatGauge("gochat_threads_count", uint64(runtime.NumCPU())),
+		}
+
+		// HELP and TYPE annotations
+		help := []string{
+			"# HELP gochat_go_goroutines Number of goroutines currently running",
+			"# TYPE gochat_go_goroutines gauge",
+			"# HELP gochat_go_memory_alloc_bytes Bytes of allocated heap objects",
+			"# TYPE gochat_go_memory_alloc_bytes gauge",
+			"# HELP gochat_go_memory_sys_bytes Bytes obtained from system",
+			"# TYPE gochat_go_memory_sys_bytes gauge",
+			"# HELP gochat_uptime_seconds Application uptime in seconds",
+			"# TYPE gochat_uptime_seconds gauge",
+		}
+
+		output := ""
+		for _, h := range help {
+			output += h + "\n"
+		}
+		for _, m := range metrics {
+			output += m + "\n"
+		}
+
+		c.Header("Content-Type", "text/plain; version=0.0.4; charset=utf-8")
+		c.String(http.StatusOK, output)
+	}
+}
+
+func formatGauge(name string, value uint64) string {
+	return name + " " + formatValue(value)
+}
+
+func formatCounter(name string, value uint64) string {
+	return name + " " + formatValue(value)
+}
+
+func formatValue(v uint64) string {
+	// Simple uint64 formatting without strconv dependency
+	if v == 0 {
+		return "0"
+	}
+	result := ""
+	for v > 0 {
+		digit := v % 10
+		result = fmt.Sprintf("%d%s", digit, result)
+		v /= 10
+	}
+	return result
+}