The external enclosure maybe faulty and are sometimes not the best places to test a drive. Take the HDD out of the enclosure and plug directly into the main board. See if you can access it then.
It looks like your only route is professional data recovery like uFlysoft:
Step 1. Launch the software to scan the device where your files deleted
Step 2: Preview the scan result files and make mark if it is the one you find
Step 3: Recover files