Unciv is open source Civ with mod support. Rogue Adventure is a really good card game that I think has a free version, but they’ve been adding features for years now. It’s kinda like Slay the Spire with simpler graphics

Mindustry always gets mentioned here, it’s a 2D automation tower defense game with a pretty cool campaign and a tech tree to keep you busy.
Pixel Dungeon and its mods also are commonly mentioned, it’s a pretty challenging old school RPG.
Stormbound is a pretty interesting PVP card game, I used to play it a lot a long time ago, don’t know if they made it P2W at some point. It’s kinda like a simpler version of Hearthstone but with positional/board game mechanics.

Edit: Forgot to mention good idle games:
Realm Grinder - Extremely long idle game that you can play for literal months and still have tons of new stuff being unlocked continually. The P2W mechanics are pretty unnecessary and don’t really matter, except making some achievements slightly easier to get.
Antimatter Dimensions - Also very long, with no P2W at all basically, and very cool prestige mechanics.
Clicker Heroes - Much more P2W and similar to the usual mobile game slop, but worth mentioning because it does have some pretty sick prestige mechanics that add a lot of depth.

Mini Metro- I guess this would be kind of a puzzle game. You connect stops on a metro and have to make sure that the passengers don’t have to wait too long for the train.

Dicey Dungeons is a great fit on mobile and has an A+ soundtrack

Ascension is one of my favorite deck building games, and the mobile version is good

Any of the Kairosoft games! The paid ones are full ass games. I usually get anywhere from 10-30 hours out of one.

Bunch of fun themed simulation games. Ive given them hundreds of dollars at this point, in even double dipping a little because they’ve been porting their games to steam.

Dungeon Crawl Stone Soup. It’s not made for phones, but if you can get past the interface it’s an incredibly deep classic rogue-like.

I bet OpenMorrowind is super good with touch controls

Luck Be A Landlord is really quite fun. It’s a very simple game concept with a luck/roguelite approach that makes for a pretty complex strategy. Every choice you make requires you to balance opportunity costs, short-term and long-term strategy, and you have to consider the likelihood of achieving your ideal endgame vs what you’ve been dealt so far.

Either you’ll develop a serious appreciation for the game in the space of 30 mins or you’ll just outright hate it. Also, with a name like that, I’m not going to tell you whether this game exists in the trashcan of liberal ideology or if it’s low-key incredibly based.

I think it’s available on Steam so if you don’t want to spend money just to take the game for a spin, there’s the Steam refund option available. The game is made by a single indie developer who is neurodivergent so they get all the love and support from me.

Vampire Survivors is another indie game cult classic. Also available on PC afaik so the stuff above applies here. It’s a massive throwback to old games but it’s very fun and my god does it all get a bit postmodern and chaotic with breaking the grammar of games in the later stages, in a way that screams “AAA game companies would never”.

Super Auto Pets is a cute little combat rougelite that is very self-contained, basically the opposite of Vampire Survivors, and it can be good fun if it’s your jam.

Slice & Dice is very polished game which I think is indie as well. Super steep difficulty curve and the luck mechanic is pretty punishing but it’s a good way to kill a few minutes here and there. I wanted to love it but I only ever got to appreciating it although it gets a lot of love from avid fans.

Fallout Shelter is supposed to be really good too but I haven’t bothered to learn how to play it yet.

Night of the full moon appears to be somewhat similar to Reigns from first glance. The difficulty is pretty low and it’s pretty fun. Might be up your alley.

Same goes for Underhand.

Papers Please gets a lot of love. I think it’s gonna be a bit lib because thematically it’s like an fetishistic westerner’s gaze of a fictitious Orwellian-themed Eastern European country existing behind the so-called Iron Curtain. Doesn’t mean that it won’t be fun but you probably need to switch that part of your brain off if you play it. It’s not like I refuse to play chess based on my principles of an anti-feudalism position, y’know? I never bought it because I feel like I’m just too ADHD to really get excited about a game which is pretty complex and which requires a strong eye for detail, but I’ve never actually played it so idk.