I think that should work when you use the Instructons for Ubuntu 22.04 LTS. There is listed Mint 21 and there stands in the Brackets that the Instructions for Ubuntu 22 should be used). So, Mint 21 is based on Ubuntu 22 LTS and Zorin, too.
I think, you should take a Look at the List for the supported Browers, too.
I agree, both Ubuntu 20.04 and Ubuntu 22.04 are listed as officially supported. This means that Zorin OS 16 and Zorin OS 17, respectively, are probably also compatible.
As for the browser, I would recommend Brave. Just make sure to not: