Generally you install software from the app store, which is called "Discover" in Ubuntu. However, the newest version of Thunderbird hasn't been shipped out there yet, so you might have to wait a day or two. It is available as a candidate release though, so if you want to try out Thunderbird 102 right now, you can open a terminal and type:

sudo snap install thunderbird --candidate

And yeah, I think it is a mistake for the Thunderbird website to not guide people to the software center.