How do I recover my lost Photos on my old iMac?

One possibility is that you've accidentally created an empty Library, and the other Library is still there, somewhere.

To look for Libraries, close Photos, and option click the Photos icon-- you should get a dialog like this:

As you can see, I have several Libraries. If you find that you have more than one, you can try choosing a different Library to see if it has your pictures. Below the list, you can also see the path to the location of any Libraries you find.

"Photos Library.photoslibrary" is the default name for a Photos Library. You should look in the Trash to see if a photoslibrary has escaped to there.

I'm not sure of anyplace else to look. Let us know what you find…

How have you been searching? If you have Find Any File use it to search for photo libraries.

You can search on both your Macs for photo libraries using the Finder.

Try the following:

• Open a Finder window and select your computer in the sidebar.
• Enter the shortcut ⌘F to start a search
• Enter .photolibrary into the search field and hit return.
• Select "Kind Photolibrary" from the search options.

For example:

Did you previously use an external disk with your old iMac? Then you may want to search all your external drives for your iPhoto Library as well, that you may have been using with the old computer.

Here is a link on how to import photos from an iPhoto Library into a Photos Library (on your new iMac): Import photos from another library in Photos on Mac - Apple Support

Which system version is running on your old iMac? If you still can run iPhoto on that Mac the system version is macOS 10.14 Mojave or earlier, right?

If all fails you may want to take that external drive to a service for data rescue. But it might be very expensive.

If you have your iPhoto library, then, while it doesn't "migrate" in the last few OSs, the pictures can be imported.