Shotcut uses ANY font installed in the fonts folder on your system. If you want to add a font, download it, and install it into the system fonts folder and it will show up in the fonts dialog when you add text.
This is going back to my graphic design days, but I think at this point, there are generally 3 kinds of fonts: Open Type fonts, True Type fonts and Postscript fonts. I think you should be cautious of downloading Postscript fonts because from what I see, only Open and True Type fonts work on Shotcut.