Interesting indeed. I had to unlock bot extra layers first.
Then, using Global Edit with the larger square selected, I get the message. With all the big squares selected, it’s 208 paths only.
I assume it does count the smaller squares as well, because if I select smaller squares and hide/lock/delete them, larger squares get selected fine. Feels true to the hypothesis, since the file has 1414 of all the square tiles, both small and large.
So despite the options say Match Appearance and Size, GA has to find all first and then filter...

This one is peculiar in that it didn't want to count anything at all. Here is a file that I created awhile ago wouldn't count over a couple hundred, so I broke it up into separate layers that had less objects.

It's even stranger than that.
In my original test, I started deleting rows one at a time, checking the function after each deletion.
Each time I got the same message.
I could get down to about 50 circles left, but the AI would still give me this error, as if I had more circles on the canvas.
After I saved a document and reopened it — it came to its senses.

I wonder why it works in one file and not the other.

Anyway, your solution is what I was looking for in the first place! Thanks so much.

I see! Now that's interesting.
I made some tests. I removed all the layers except the current one, and then removed some rows, to get only 27 rows. 39 × 27 = 1053.
Now, when I try to Global Edit a gray circle, I still get the warning. But if I remove one more row (which makes it 1001 circles), I don’t get one!
So I think Ai tries to search for ALL duplicates first and then filter them by appearance, if the option is chosen. The message is wrong then... not 'highlighted' objects, but 'processed' or something like that.
...or perhaps it’s something more weird than this. Either way, worth investigating further. Thanks!

As a workaround I advise you to open the Document Info panel, and choose Objects in its menu.
Then it will quickly count the selected objects, with no limitations Global Edit has.

Oh. Here is the actual file that didn't work.

It worked fine yesterday and today on this file and another similar file (globaleditworks). But not at all on this file (globaledit) and another similar file. I tried restarting Illustrator and restarting the computer.

Denise, can you reproduce this problem in a new document with a roughly same amount of similar objects?
If not — can you share the original file?