Hi Charles.
Leave it alone for another 48 hrs to see if the "Emptying Bin" manages to complete, remember that this is all happening on the external drive, the "Bin" referred to is not the Bin on your Mac but a temporary bin on the external hard drive.
Stopping a delete process on an external hard drive always risks the disk file index being damaged and then you won't be able to access any files on the drive.
After 48 hrs if no further progress then try to transfer the files you need to save to another external disk, try to avoid transferring to the internal Mac disk if at all possible as this may cause the Mac to crash if it has a stuck delete process in the process stack.
If, after 48 hrs the Mac is still non-responsive, the emptying bin process has not completed and you are unable to transfer the files off that disk then you have no other option but to force the delete task to quit by initiating a restart, but please note this may result in the external disk being unreadable after the Mac is rebooted.
When a restart command is issued it may still take a long time for the Empty Bin process to halt and release the Mac to obey the restart command, don't be surprised if it takes up to an hour after ordering the Mac to restart and the Mac actually does restart and during that time the cursor will show the spinning beach-ball icon.
If the Mac has not restarted after an hour then hold the power button in until the Mac is forced to close.
Before restarting disconnect the external disk.
After a forced power-down it is best practice to boot into Safe Mode first, then after the long boot-up that Safe Mode requires reboot again into Normal Mode.
Here is a list of key combinations that include the Safe Mode start-up:
https://support.apple.com/en-gb/HT210898
Once the Mac is running in Normal mode you can reconnect the external disk and hopefully your files will still be accessible.
If there are any issues accessing those files on the external disk after the forced shutdown then use Disk Utilities and run First Aid on that external disk.
Always run First Aid in the sequence Volumes first, then Containers and finally Disks, running First Aid in the opposite direction is less likely to successfully fix all errors present.
See this document for guidance on Disk Utilities and running First Aid:
https://support.apple.com/en-gb/HT210898
After successfully transferring the files elsewhere that you want to keep then you could reformat the drive to ensure the file indexes are cleared properly and fee space recovered.
Finally, if the drive has been used continually for Time Machine backups and is > five years old then the drive is nearing its expected end of life anyway and should probably be replaced to ensure reliability for the future.
HTH
Will.