Rename express/ to backend/ and update references

Update paths in sync.sh, master/main.go, and CLAUDE.md to reflect
the directory rename.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/biome.jsonc

@@ -0,0 +1,39 @@
+{
+    "$schema": "https://biomejs.dev/schemas/2.3.10/schema.json",
+    "vcs": {
+        "enabled": true,
+        "clientKind": "git",
+        "useIgnoreFile": true
+    },
+    "files": {
+        "includes": ["**", "!!**/dist"]
+    },
+    "formatter": {
+        "enabled": true,
+        "indentStyle": "space",
+        "indentWidth": 4
+    },
+
+    "linter": {
+        "enabled": true,
+        "rules": {
+            "recommended": true,
+            "style": {
+                "useBlockStatements": "error"
+            }
+        }
+    },
+    "javascript": {
+        "formatter": {
+            "quoteStyle": "double"
+        }
+    },
+    "assist": {
+        "enabled": true,
+        "actions": {
+            "source": {
+                "organizeImports": "on"
+            }
+        }
+    }
+}