It works for me on Ubuntu 20.04. Perhaps there’s an incompatibility with the graphics driver, I really don’t know. When running it from the command line:
$ snap-store
18:52:39:0155 Gs enabled plugins: odrs, rewrite-resource, snap, icons, key-colors, key-colors-metadata
18:52:39:0155 Gs disabled plugins: appstream, desktop-categories, desktop-menu-path, dpkg, dummy, epiphany, fedora-pkgdb-collections, generic-updates, hardcoded-blacklist, hardcoded-featured, hardcoded-popular, modalias, os-release, provenance, provenance-license, repos, shell-extensions
18:52:43:0007 Gs failed to create an app for */*/*/*/system/*
18:52:43:0010 Gs updates-shell: failed to get updates: no plugin could handle get-updates
18:52:43:0010 Gs failed to create an app for */*/*/*/system/*
18:52:43:0010 Gs failed to get system app
18:52:43:0010 Gs Only 0 apps for recent list, hiding
18:52:43:0030 GsPluginSnap Failed to load snap icon: local snap has no icon
18:52:43:0300 Gs hiding category graphics featured applications: found only 0 to show, need at least 9
18:52:43:0322 Gs hiding category audio-video featured applications: found only 0 to show, need at least 9
18:52:43:0449 GsPluginSnap Failed to load snap icon: local snap has no icon
18:52:43:0487 GsPluginSnap Failed to load snap icon: local snap has no icon
18:52:43:0710 GsPluginSnap Failed to load snap icon: local snap has no icon
18:52:44:0578 GsPluginSnap Failed to load snap icon: local snap has no icon
Do you you see different error messages that might give a hint?