Looks like a great start! If I had any feedback just from glancing at it, it would be that the transitions from desert to other climate types are rather abrupt in places- the quick shift from humid continental in the northern part of the major supercontinent and to tropical rainforest in the southern part leap to mind. Generally deserts are surrounded by fairly wide bands of semi-arid climates such as steppe or Mediterranean climates. The other major comment might be that at the moment the mountainous areas seem to be quite narrow, more so than they would be on Earth (though it's hard to tell without an elevation map). Earth has quite large areas of highland climates which don't appear here- not sure to what extent those figure into the Artifexian tutorial however.

Depending on how much time you're willing to dedicate here, I will say that the tutorial here on Cartographer's Guild put together by Azelor (with many inputs from Charerg and Pixie, among others) is somewhat more comprehensive, and the results I've seen from it tend to look somewhat more plausible to me. Of course, it also involves elevation, temperature, and precipitation maps, which take even more time! The detail you can put into climate modeling is limited only by the amount of time you're willing to dedicate to it!