Before your ticket is assigned to one of my colleagues, I'd like to guide you through some initial debugging steps to expedite the support process.
Could you please follow the below steps and let us know how it goes:
1. Could you please try another browser and see if this resolves your issue?
2. Do you see any errors on the browser console when you try to press the “Search” button from the WPML >> String Translation page?
3. I’ve tried to reproduce this issue at a fresh WP site and it seems to be working correctly so it might be due to some possible theme/plugin conflict on your site. If you have a staging/test site then you can isolate the cause of this issue by deactivating all plugins except WPML and with the default WordPress theme like Twenty Twenty-Three. If the issue is gone activate each plugin one by one to see which one causing this issue.