OK. I got the snap store running for Ubuntu 20.04 using:
$ snap refresh snap-store --channel=stable/ubuntu-20.04
Although snap-store seems to work properly again. I get a lots of messages in /var/log/syslog when launching snap-store. Not sure if they are (all) snap related however…
gnome-shell[6748]: JS ERROR: TypeError: this._workspacesViews[i] is undefined#012_syncWorkspacesActualGeometry@resource:///org/gnome/shell/ui/workspacesView.js:782:13#012_updateWorkspacesActualGeometry@resource:///org/gnome/shell/ui/workspacesView.js
=== looks like a gnome-shell workspace issue ===
dbus-daemon[6077]: [session uid=1000 pid=6077] Activating service name=‘org.gnome.Nautilus’ requested by ‘:1.24’ (uid=1000 pid=6748 comm="/usr/bin/gnome-shell " label=“unconfined”)
=== not sure what Nautilus has to do with snap, but looks apparmor unconfines it. Not an error I think ===
kernel: [ 4154.687617] audit: type=1400 audit(1602192970.273:9661): apparmor=“DENIED” operation=“open” profile=“snap.snap-store.ubuntu-software” name="/var/lib/snapd/hostfs/usr/share/mime/mime.cache" pid=28733 comm=“snap-store” requested_mask=“r” denied_mask=“r” fsuid=1000 ouid=0**
=== here apparmor denies snap-store (?) to open a mime.cache. Looking at my previous reply, do I have caching issues? ===
gnome-clocks[29346]: Theme parsing error: :1:0: Failed to import: The resource at “/org/gnome/clocks/css/gnome-clocks.yaru-dark.css” does not exist
=== Not important ===
gnome-shell[6748]: Received error from D-Bus search provider org.gnome.seahorse.Application.desktop during GetResultMetas: Gio.DBusError: GDBus.Error:org.freedesktop.DBus.Error.UnknownMethod: No such interface “org.gnome.Shell.SearchProvider2” on object at path /org/gnome/seahorse/Application
gnome-shell[6748]: Wrong number of result metas returned by search provider org.gnome.seahorse.Application.desktop: expected 1 but got 0
=== Graphics issue? No complaints there, so lets leave this for now. ===
kernel: [ 5268.346963] audit: type=1400 audit(1602194083.943:11264): apparmor=“DENIED” operation=“open” profile=“snap.snap-store.ubuntu-software” name="/var/lib/snapd/hostfs/usr/share/mime/globs2" pid=29422 comm=“snap-store” requested_mask=“r” denied_mask=“r” fsuid=1000 ouid=0
=== … and a lot apparmor denied lines. It does not seam to have impact on the store. /var/lib/snapd/hostfs is an empty folder. ===
For me it looks like I can proceed to reinstall all snap packages which where removed during the “purge” 
Unless I should really look into one of the above errors, you may mark this issue as solved. Thanks for your help! 