That's a cache, though, when the use case at hand is random access.
I mean, if I'm willing to do some prep work I can surely do even better than sticky notes (like, heh, "google for all the monsters ahead of time and line them all up in browser tabs").
How DMs prepare, if they do, is highly variable. But most DMs choose monsters ahead of time. This appears in survey data in The Lazy Dungeon Master. The questionnaires are interesting, when asked how they would prepare for a session if they only had 30 minutes, most DMs explicitly mentioned choosing monsters.
Over the years, my personal experience is that running things out of the browser or PDF is great if you need to search for random rules and other situations that come up during the game, but paper books and notes are overwhelmingly superior for expected conditions like encounters and monsters. I've used various laptop systems (wikis, docs, text files), apps, and paper systems (typed, handwritten, paper or notecard). On the balance of things I decided that running the game with a laptop was worse than running a game without one, at least the way I play the game.
That's just a personal choice, but it seems like most DMs do choose monsters ahead of time.
I've been running the old d20 Star Wars game for my kid, and with PDFs of all the rulebooks, one of my main game prep things is printing out the pages for the creatures / characters / spaceships I think are likely for a session.
