Asklemmy

A lot of really good older games have been ported to mobile and work fantastically. Knights of the Old Republic, Neverwinter Nights, and Baldur's Gate just to name a few. Hell, you can play Baldur's Gate multiplayer, cross-platform with PC players even! There's also fo2.exe on the Play Store, which lets you play Fallout 1 & 2 on mobile provided you have access to the files from the PC versions. Oh, and Doom ports galore, of course.

As far as mobile-only or mobile-specific games, my favorite is probably Caves, a surprisingly well done and completely free roguelike.

Also an honorable mention goes to Organ Trail, a zombie-themed take on Oregon Trail that is, frankly, just a flatly better version of the game in almost all regards. The only reason it's not my favorite is because the controls on mobile feel awkward compared to the PC version. Still fun though.

Slay the Spire is excellent on mobile, it's a roguelike deck builder.

Marvel Snap is a really fun lightweight TCG kinda thingy. I never liked Hearth stone or Runeterra, however I thoroughly enjoy Snap

Might not be the answer you expect, but I have an iPhone and I got myself an Apple Arcade subscription without expecting much (I didn’t play mobile games at all before that, because they tend to feel either unoriginal, or scammy, or both), and I was surprised at how most games (not all games, but still) were truly original, and none of them were scammy since I was technically paying for them with the subscription. It’s been a surprisingly nice exploration.

Night of the Full Moon

Unciv is an open source Civilization (5? 6?) clone without the heavy graphics. I'd probably play it if I were more into phone usage.

Farm RPG

N.O.V.A 3 (Near Orbit Vanguard Alliance). It is a mobile FPS with a pretty good campaign. Bonus points if you can find it without ads.

I am playing a lot of slice and dice right now. Rogue-like dice rolling game. Available for PC and mobile. Free demo available. If you buy it on Itch.io you get a code for activating your mobile download as well. Absolutely worth the 7 dollars I spent on it.

Shattered Pixel Dungeon

On iOS, there's an AltStore app called PojavLauncher. It's a launcher for Minecraft Java Edition, which is pretty awesome.

I also quite like the original Angry Birds (now called "Red's First Flight"), but that's £0.99.

On Android, have a look at the games category on F-Droid.

Magic the Gathering: Arena. The mechanics for getting gold, packs, and cards uses semi-toxic dailies/weeklies, but it's do-able to play free2play.

Definitely the mobile version of Stardew Valley

I used to play a ton of rocket league on pc. I was upset at one point by some of their decisions. However i have really been enjoying their free mobile game rocket league sideswipe. It’s different than other games so that ticks the box and there is a lot of room to grow skill wise.

World of tanks blitz is amazing.

So is my heroes for RPG

Cytus II, it's a great rhythm game with a cool storyline

One More Line is pretty great.

May be the commercial one but actually Candy crush is a nice one