I have been facing the annoying issue of touchpad presses while typing since my last reinstallation. I had never faced a similar situation before (or I never noticed). The disable-while-typing gnome dconf was set to false. The issue was apparently with libinput not recognizing my touchpad as internal. Thankfully, that can be fixed with a quirk file. This askubuntu answer further clarified on how to write the quirk.

On the side note, I figured out how to disable the touchpad while I am using an external mouse.

gsettings set org.gnome.desktop.peripherals.touchpad send-events disabled-on-external-mouse

Although it sucks that this is not something I can just use the settings GUI for, I am glad I could figure it out before I lost my mind! ;)