chore(backend): update template to v0.6.0, conflicts left

backend/CLAUDE.md

@@ -1,7 +1,8 @@
 ## Checking commands
 After writing code, always run from `backend/`:
 ```shell
-ruff format
-ruff check --fix
-ty check
+make fmt
+make check
 ```
+
+Mind startup imports: `make check` runs `scripts/check_imports.py`.