It used to work with Install Linux apps using the Snap Store | Snapcraft but not any more as the output is just blunt Showing 1 to 15 of over 100 results for " " -but there us not total number like before.
Or is there some other way to get the total number of snaps in Snap Store fast?
Not that I’m aware of. There isn’t a good single number, either. There are test snaps (which you wouldn’t want), private snaps (you can’t see), duplicate snaps (same application, multiple publishers) and unlisted snaps (which don’t show up in search), and ones which are only available for architectures you don’t use (so you can’t install).
One rough number that I find a good hand-wavy figure is the output of wc -l /var/cache/snapd/names on an amd64 system. Which at the time of writing is 6398.
However, that number is rough for the reasons above.