Register password at login

Make it so when you’re Zorin PC is locked, and you start typing (your password), it registers. Video illustration:

This is a GDM3 thing.
I am using LightDM and on mine, it registers my password the moment I begin typing, even while the screen is still off. It is not unusual that I type my PW, hit enter and a moment later, the screen powers on with the computer logged in / unlocked.

How do I remove GDM3 and installDM? Would this break Zorin in any way?

LightDM is used by default in Zorin Lite. And on most XFCE distros.

Yes, you can install LightDM without breaking Zorin OS. You may also use SDDM, I believe.
You can install with the terminal:

sudo apt-get install lightdm

During the installation, it will ask if you would like to switch. Say yes.
Otherwise, you can switch between Display Managers in the terminal

sudo dpkg-reconfigure gdm3
sudo dpkg-reconfigure lightdm
sudo dpkg-reconfigure sddm