Got a bit carried away, but hopefully this is useful to somebody:
The Steam Deck is surprisingly versatile, especially now Valve have released the dock (enabling portable monitors). The most obvious benefits over a gaming laptop (beyond the price) are the smaller form-factor and relative quiet compared to a strong gaming laptop.
The main thing you should ask yourself is what you want to play.If your answer to that looks like "Crusader Kings III, Dota 2, and the latest competitive shooter", then it might not be the best choice. But in general, you'd be surprised by how many games work great thanks to its extremely versatile input options.
Games that released before controller support on PC was mainstream -- such as Oblivion, S.T.A.L.K.E.R., Deus Ex, or Baldur's Gate -- typically play fine thanks to its extensive input customisation (including custom radial menus), its dual trackpads and gyroscope, and the community layout system. There are exceptions where you'd want a keyboard and mouse, but not as necessary as you'd expect.
Beyond info on software compatability, ProtonDB also includes Deck-specific reports at the top of each page detailing others' experiences, such as whether they used a specific community layout or input method, performance under specific conditions (such as limiting power or frames to conserve battery life), and legibility on a smaller display. The wealth of shared controller configs is easily one of the greatest strengths the Deck has.
(And while other, more recent -- albeit more expensive -- options have stronger performance at higher power settings, the Deck has a strange persistence in outperforming its competitors at low power settings (source).)
Again, it's mostly down to what you want to play. If you want to play recent releases with all the bells and whistles enablesd, you'd need to pay for a laptop many times the cost of a Deck (desktops less dramatically). Given you're even considering handheld PCs I'm assuming that's not your priority. Cyberpunk and the ever-demanding Red Dead Redemption 2 have been in the top 20 most-played games on Deck since Valve started publishing that information, so simply playing them isn't an issue. (The top 100 games for 2023 by daily active players can be seen at the bottom here.)
To address some specific games and genres: If you're into MOBAs, League and Dota play fine but you'll want to be using a keyboard and mouse, while grand strategy games would at least warrant an external display.
If you want to play the latest CoD multiplayer, Valorant, or the upcoming Tarkov Arena, you should probably get a laptop. (You can install Windows on the Deck, but I can't speak to that firsthand.) The trackpads themselves are viable for FPS games, though a learning experience, but the main issue here is that most developers haven't enabled the option for their anti-cheat to work on Linux. Hunt: Showdown is a happy exception to this trend.
If you want to play MMOs, it'll depend heavily on the individual game. FFXIV has excellent controller support out of the box (Gabe Newell spent covid playing it on Deck), Path of Exile added strong controller support to improve experiences on Deck, and ESO reportedly runs great. People have made Guild Wars 2 work, as well as WoW via the impressive ConsolePort addon, but it won't be as clean an experience. The more niche, the more trouble it'll be. The problems here are universal to handheld PCs, and with MMOs you also need to consider whether you'd need a keyboard for social reasons. The Deck's on-screen keyboard is pretty decent, but it's not going to be a substitute for a real keyboard.
Almost any singleplayer RPG, FPS, or adventure game can be made to work just fine. Emulation has EmuDeck and can play most older games -- assuming general emulator compatibility -- up to some PS3 titles (like Demon Souls, Kingdom Hearts HD 1.5 Remix, or the MGS HD Collection) and even a lot of Switch titles. Traditional roguelikes include many among the few 2D/singleplayer titles that don't simply work out of the box. Yet a substantial number play great (e.g. Jupiter Hell, Tangledeep, Shiren the Wanderer, Caves of Qud); and many others have community layouts already so you don't have to take the time to set one up yourself. It was learning that Dwarf Fortress played fine on Deck that opened my eyes to just how flexible the chunky little handheld can be.
I hope that helps in determining whether the Deck suits your personal needs; if there's any angle I didn't cover adequately that you have questions about, please feel free to ask.
Edit: Slight clarification, re: "Almost any singleplayer RPG, FPS, or adventure game" -- this year, many multiplatform games have released on PC in a poorly optimised state, and depending on your personal tolerance the Deck may struggle to provide an adequate experience for them. Though it's hard to give a recommendation in one direction or the other without knowing your budget, as such titles are often found lacking on even the newest consumer desktop hardware (hardware very few laptops can compare directly against, and so many will suffer these issues in a similar manner). A relevant Digital foundry video: https://www.youtube.com/watch?v=oav-pZyA8y4