Playing the snare
Because finger-drumming on a gamepad is miserable.
Controversial opinion I know, but snares aren't actually all that interesting most of the time. That doesn't stop them from being important: they're the metronomic thing that anchors the groove, the thing that makes your head nod, but 99% of the time they're stuff you want to keep going while you're doing something else, so Drums leans into that.
Backbeat, which you can find on the Play tab of the Drums panel, has two modes. Neither is better than the other, it's more about how you want to play it. Both fundamentally do the same thing: play the snare where the snare should be, most of the time.
Automatic
Automatic brings the snare in on the backbeat (the 2 and 4 in 4/4) whenever either of the analog sticks are pushed out to their edges. While you hold a d-pad direction, that pattern takes over the snare, and the backbeat comes back when you let go.
Manual
Manual puts the snare on the right trigger R2 instead. Hold it to play the snare on the backbeat.
Rolls, and other things snares can do
Backbeat is most of what snares are used for, but when you need them to do something else it's useful to have them do it precisely, and generally speaking pretty quickly. That's where the D-pad comes in.
Unless you are a member of a distant future offshoot of humanity that accidentally time-traveled back to 2026, or have a fortuitous but socially awkward mutation that gave you two prehensile thumbs on one hand, you can't control the D-pad and the left analog stick at the same time on any gamepad. That kind of means that snare rolls and hi-hat patterns are mutually exclusive. But that's okay! Because that's, generally speaking, the way drummers tend to play these kinds of things. They switch between them fast when they need to alternate, which is why the snare and the hi-hat share a thumb in MIDIpad - with a little practice you can snap back and forth between them and they complement one another without compromising either.
Keep moving
Drums is supposed to be played like Mortal Kombat, not like a rhythm game, and the snares on the D-pad are where that's more true than anywhere else I think. Go for uppercuts rather than just jumping.
The D-pad picks patterns the way the sticks pick rhythms, but it's designed more for stabs than for constant rhythm. Try rolling your thumb across the D-pad in circles, or across it diagonally, to get a feel for the kinds of patterns that fall out of it.