Try Data Rescue. It has been years since I used it, but I think it may allow you to select a drive.
I know that TestDisk and PhotoRec can be used since they insist the drive is unmounted first, but I believe they are both command line utilities. I've only ever used TestDisk though and it can be confusing on how it works. I don't know how either utility works with an APFS file system.
What file system is being used on the external drive?
FYI, it sounds like your drive may be failing. If that is the case, then do not use any data recovery apps as they will be unable to handle the errors produced by a failing drive. Data recovery apps are only meant to recover accidentally deleted data from working drives. Using a data recovery app, or any app to attempt to recover data or fix the drive will result in the drive failure getting worse since most utilities don't know how to handle the errors.
You can attempt to check the health of the drive by running DriveDx. You will need to install a special USB driver in order to attempt to retrieve the health information from the external drive. However, even with the special USB driver some external drive enclosures will not allow the necessary communication to access the drive's health information. Post the complete DriveDx text report here using the "Additional Text" icon which looks like a piece of paper.