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/api/v1/contact_inbox_handler.go

@@ -0,0 +1,67 @@
+package v1
+
+import (
+	"net/http"
+	"strconv"
+
+	"github.com/gin-gonic/gin"
+	"github.com/gochat/gochat/internal/service"
+)
+
+// ContactInboxHandler handles contact_inbox-specific API endpoints
+// that are not nested under a single contact (e.g., filter by account).
+// Reference: Chatwoot app/controllers/api/v1/contact_inboxes_controller.rb
+type ContactInboxHandler struct {
+	svc *service.ContactInboxService
+}
+
+// NewContactInboxHandler creates a new ContactInboxHandler.
+func NewContactInboxHandler(svc *service.ContactInboxService) *ContactInboxHandler {
+	return &ContactInboxHandler{svc: svc}
+}
+
+// Filter retrieves contact_inboxes by account with optional filters.
+// GET /api/v1/accounts/:id/contact_inboxes/filter?inbox_id=...&contact_id=...&source_id=...&page=1&page_size=25
+// Reference: Chatwoot contact_inboxes_controller#filter
+func (h *ContactInboxHandler) Filter(c *gin.Context) {
+	accountID, err := parseUintParam(c, "id")
+	if err != nil {
+		c.JSON(http.StatusBadRequest, gin.H{"error": "invalid account id"})
+		return
+	}
+
+	page := getPage(c)
+	perPage := getPageSize(c)
+	offset := (page - 1) * perPage
+
+	// Optional filter params
+	var inboxID, contactID *uint
+	if v := c.Query("inbox_id"); v != "" {
+		id, e := strconv.ParseUint(v, 10, 64)
+		if e == nil {
+			uid := uint(id)
+			inboxID = &uid
+		}
+	}
+	if v := c.Query("contact_id"); v != "" {
+		id, e := strconv.ParseUint(v, 10, 64)
+		if e == nil {
+			uid := uint(id)
+			contactID = &uid
+		}
+	}
+	sourceID := c.Query("source_id")
+
+	contactInboxes, total, svcErr := h.svc.FilterContactInboxes(
+		c.Request.Context(), accountID, inboxID, contactID, sourceID, offset, perPage,
+	)
+	if svcErr != nil {
+		c.JSON(http.StatusUnprocessableEntity, gin.H{"error": "failed to filter contact inboxes"})
+		return
+	}
+
+	c.JSON(http.StatusOK, gin.H{
+		"contact_inboxes": contactInboxes,
+		"meta":            gin.H{"count": total, "page": page, "page_size": perPage},
+	})
+}