Cannot install GnomeTweaks due to broken packages

The dependencies seem to be broken. I already tried fixing those without success.
Anyone had the same problem?

Can you open Software & Updates from the Zorin Menu. Or launch with alt+F2 and enter in software-properties-gtk and hit enter.
On the first tab, under Download From, select main server from the drop down menu.

Then in terminal, run:

sudo apt install -y gnome-shell-extension-prefs gnome-tweaks

Software & Updates won't launch.
Also won't work with alt+F12.

Is this a fresh installation- default, or have you added or removed any software?

The installation was done just yesterday.
I installed only a few applications (Spotify, Teams, Discord etc.).
Nothing that would change critical files.

Well the symptoms you are describing are pretty severe. There is something corrupted either in the installation or from the original download of the .iso.
Unpleasant it may be, I strongly suggest a full reinstallation of Zorin OS. It's the best way considering it is a fresh installation and various facets of Gnome are clearly broken - sussing them all out would be uncertain and unstable and far more work.

sudo apt --fix-broken install

Then try