App updates not listed in apt list --upgradeable

I am an amateur Ubuntu user and recently I've noticed two things:

• whenever I open DBeaver, it prompts me to install a new minor version; when I click the button, I get redirected to the DBeaver website and need to manually download the new update
• apt list --upgradeable does not list DBeaver updates

I installed DBeaver via Ubuntu "Software" utility, my OS: Ubuntu 18.04.2 LTS x86_64, kernel: 4.15.0-50-generic.

Is it possible to configure an app to be updateable via sudo apt update along with other updates, if it's not by default?

The screenshot in your question shows that you have the dbeaver-ce snap package installed. Packages that were installed by apt and snap packages are upgraded by two different commands from the terminal. apt list --upgradeable shows only the upgradeable packages that were installed by apt. To upgrade all snap packages run sudo snap refresh

Software Updater also only updates installed apt packages. Installed snap packages are automatically updated separately in the background. If there are snap packages that require authentication in order to be upgraded the Software app shows a notification that updates for snap package(s) are available. Clicking the notification opens the Software app with a small authentication window in front of it.