As discussed during the chat the issue seems to be interference from some thirdparty plugins or theme/code, please follow the following steps and see how it goes:
- Backup the site completely even though it is a staging site to prevent any issues and data loss.
- Deactivate all plugins except WPML plugins and activate a default theme like twenty twenty one then see if you can translate strings at WPML -> Strings Translation
- If it works, please activate the original theme and plugins once at a time , each time testing the issue to find which start the issue again.
Please let me know how the test goes and we can further look into the if required.