You can use package management tools on your system (
aptitude etc) but they're not online and not stores (they're package managers ; deal only with deb packages, and allow searches).
You can use a browser to look up what's available - but it's not in one location; eg. use GNOME's web pages for GNOME apps; KDE pages for KDE apps etc... but each only offers details about it's own packages (the Ubuntu Software Store combines them into the one location on your machine but you don't want to use that).
ie. they're managed by the various Projects that create them, and not in a single managed store; that's done on your machine in the program you don't want to use.
Other stores exist too, Software Boutique, Discover etc. but some of those include snap and other packages too.
I use CLI tools (
apt search etc), but the online equivalent of that is https://packages.ubuntu.com/ but it's not a store; just a package database. These deal with only the packages you specifically use (ie.
apt search will search for deb packages,
snap search looks for snap packages etc).