Cannot eject hard drive "because one or more programs may be using it"

To see what's running in the background to give you a possible culprit download and run Etrecheck. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

IMPORTANT:

Before running Etrecheck assign Full Disk Access to Etrecheck in the Etrecheck's Privacy preference pane so that it can get additional information from the Console and log files for the report:

Also click and read the About info to further permit full disk access.

Copy the report

and use the Additional Text button to include the report in your reply.

Then we can examine the report and see if we can determine what might be causing the problem.

Old Toad wrote:

Did you try force quitting the apps one at a time and then try to eject the drive? I'd start with a Finder relaunch.

Do you have any image editing apps that saves scratch/cache files to a preselected volume, like Photoshop, Photoshop Elements or GraphicConverter?

https://discussions.apple.com/content/attachment/b62c9a68-7d13-4cec-acb2-a4065cd6cc49

Another example of such apps that can use scratch space on an external drive is Lightroom. I have seen this with someone using Lightroom, and in some cases Adobe apps or associated processes appear to be doing some housekeeping in the background that may continue for a little while even after quitting the app.

Did you try force quitting the apps one at a time and then try to eject the drive? I'd start with a Finder relaunch.

Do you have any image editing apps that saves scratch/cache files to a preselected volume, like Photoshop, Photoshop Elements or GraphicConverter?

You might want to run Disk Utility's First Aid on the EHD and the do another Spotlight index of it to see if that will let you search the drive and unmount it when necessary without issue.

Find out which programmes are using it.

Ejecting the disk is as simple as dragging its icon to the Trash.

Or Control-clicking on its icon and selecting Eject <name of disk>.