chore: update lint scripts and improve formatting consistency

- Added `lint:fix` scripts for backend, frontend, and documentation.
- Enabled `biome check --write` for unsafe fixes in backend scripts.
- Fixed imports, formatting, and logging for improved code clarity.
- Adjusted service unit tests for better readability and maintainability.

backend/biome.json

@@ -24,7 +24,8 @@
 		"rules": {
 			"recommended": true,
 			"suspicious": {
-				"noUnknownAtRules": "off"
+				"noUnknownAtRules": "off",
+				"noExplicitAny": "off"
 			},
 			"style": {
 				"useImportType": "off"