I have a slightly different problem; AppCenter is notifying me that there are updates, and when I click on AppCenter/Installed, it shows me the updates. However, when I click on "Update all" and enter my password, in less than a second I see in this order; "Loading cache", "Finished", "Starting" and it stops, not having updated anything, still showing the same updates.

However, when I do
sudo apt-get update
sudo apt-get upgrade
it seems to work, but after that AppCenter still shows the same updates and still behaves the same. I don't know what is going on, perhaps AppCenter cache needs to be cleared, but I don't know how.
I can install other apps (I installed a simple card game successfully)
I have elementary OS 5.1 Hera, Built on Ubuntu 18.04.3 LTS, Linux 4.15.0-74- generic, GTK 3.22.30 on an HP EliteBook-840-G3 laptop.
Everything else seems to work fine.
What should I do?
Thanks