Problem solved via support. The solution was to play something (a Netflix title in my case) and unplug the mains while playing. This allegedly cleared the "cache". Et voila: the LG Content Store was working again, app updates were available and Disney+ also started working again (not sure if this was cache related or the app update).
Ofc I had power-cycled many times beforehand but it was important to be playing something while powering down, apparently.