I'm not a drummer, but my band uses ST and I can't explain what our drummer gets from the experience.
Drum Click
We use multitrack audio for all our backing tracks and a key part is having a dedicated drum click audio track just for the drummer that goes into his IEM mix. We also have a Cues track (i.e. prompts such as "drums in on 3" or "Bridge in 1 2 3 AND") that goes to all band members' IEM mix which the drummer also leverages
Lyric Sheets - https://stagetraxx.com/user-guide/lyrics/
We timestamp our lyric sheets so that all band members can glance at it and know where we are in the song.
Individual band members' can also put any critical notes into the lyric sheet (a certain fill in a certain spot, a type of unusual beat, etc.). We try not to overload them otherwise it is confusing, so we reserve it for notes that are really important (or things that individual band members' just cannot seem to remember 🙂 ). Of course, ST does give you the option to do local lyric sheets (https://stagetraxx.com/user-guide/network-sessions/#display-your-own-lyrics), and so band members can also opt to do this if they need copius notes that would just distract others. He doesn't go as far as having notation sheets for songs, just lyric sheets with any notes that make sense to him in his own 'shorthand'.
Remote Control - https://stagetraxx.com/user-guide/remote/
During a gig, our drummer controls song Start/Stop via MIDI triggers from his Roland SPD SX PRO drum sampler pad. There are a handful of songs where we also have crossfades setup that he triggers, and other songs with more complex start timings (where he documents this in the lyric sheet). Equally, we use the MIDI automation in ST to send program change messages (https://stagetraxx.com/user-guide/midi/#bank-select-and-program-changes) from ST to his Roland SPD to load the correct drum kit for each song.
Hope that helps!