This is a slightly different use of the word 'best,' not a straightforward comparison of two alternatives. 'It's best to X' means it's advisable. Here it is a little confusing because there are two choices. You could also say, 'It's better to use this tool on a desktop, not your phone.' But if you were definitely comparing two things, it would have to be: 'It's better to use this tool on the desktop than on your phone.'

Yes and no. In this context, either word feels correct to me. Rather than try to answer this myself, I'm going to quote a usage note from a dictionary: "According to a traditional rule of grammar, 'better,' not 'best,' should be used in comparisons between two things: 'Which house of Congress has the better attendance record?' This rule is often ignored in practice, but it still has many devoted adherents. In certain fixed expressions, however, 'best' is used idiomatically for comparisons between two: 'Put your best foot forward.' 'May the best team win!'" I think "It's best to..." is another example of one of these "fixed expressions." Gilgy is right, "It's best to" is an idiomatic phrase meaning "it's recommended..." Notice the writer had just said "It's best to use this tool on a desktop." they would have been perfectly correct. We can use "best" even when there is nothing explicitly being compared.

Maybe think of it this way. One option is to use this tool on a desktop, the other is to use it on your phone. Of these two options, the best option is to use it on a desktop.

You technically have a good point. Since there are only two options being offered, the rules of grammar call for a comparative adjective rather than a superlative one. But in real life, they're often used interchangeably like in your example. I'm way pickier about grammar than most people, but I wouldn't have even noticed the error if you hadn't pointed it out.