micky wrote:

A win7 question but I included win10 in case it happens there too and
because I think a lot of win7 experts now only read win10.

If I pass the cursor over a Firefox or Edge section of my task bar, a
box an inch high with a list of all the Firefox or Edge windows pops up
and stays sometimes for a long while. Other programs like Solitaire,
Eudora, Forte Agent don't do this, though they may pop up an unobtrusive
non-annoying tool tip.

Is there a way to get rid of these browser boxes?

Get WinAero Tweaker (just be sure you understand a tweak before applying
it, since some can change behavior that you really want).

https://winaero.com/

After installation, load WinAero Tweaker and enter "taskbar" in the
search box. Select the "Taskbar thumbnails" search hit. You can enable
or disable the thumbnails, change their timeout, etc. Have fun.

This makes a registry change. As JJ pointed out, this option became a
policy; however, all Windows policies are registry entries. Microsoft
even provides an Excel spreadsheet listing the policies and their
matching registry entries. A tweaker makes it easier than drilling
through a spreadsheet and using regedit.