Cinnamon's Nemo (GUI) file manager shows folder item count in the List View's "Size" column rather than a byte value. It started as a fork of Nautilus (now GNOME Files), so that and its descendents may also have the same feature.
The equivalent GNOME gio list command line command doesn't seem to do this.
It wouldn't be too hard to whip something up in Python, Perl etc. if you can't or don't want to install anything else for some reason.
is a Perl incantation that will return the number of entries in the current directory, or the supplied directory if that's added as a parameter after the command.
The -2 in there subtracts the count for . and ... That's off by one for the root directory where there's no ".." but that's rare and I didn't want to add too much for a quick proof of concept.