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/extract_routes.py

@@ -0,0 +1,37 @@
+import re
+
+with open('internal/router/router.go') as f:
+    text = f.read()
+
+lines = text.split('\n')
+
+group_prefixes = {}
+group_prefixes['engine'] = ''
+
+for line in lines:
+    stripped = line.strip()
+    gm = re.match(r'(\w+)\s*:?=\s*(\w+)\.Group\("([^"]+)"', stripped)
+    if gm:
+        var_name = gm.group(1)
+        parent = gm.group(2)
+        path = gm.group(3)
+        parent_prefix = group_prefixes.get(parent, '')
+        group_prefixes[var_name] = parent_prefix + path
+
+routes = []
+for line in lines:
+    stripped = line.strip()
+    rm = re.match(r'(\w+)\.(GET|POST|PUT|PATCH|DELETE)\("([^"]+)",', stripped)
+    if rm:
+        group_var = rm.group(1)
+        method = rm.group(2)
+        path = rm.group(3)
+        prefix = group_prefixes.get(group_var, '')
+        full_path = prefix + path
+        routes.append((method, full_path))
+
+routes.sort(key=lambda x: x[1])
+
+for method, path in routes:
+    print(f"{method} {path}")
+print(f"TOTAL:{len(routes)}")