Games

Rimworld can be played only with a mouse pretty good. And City Skylines too

1. Slay the Spire
2. Tactical Beach Wizards (on sale!)
3. Rogue Light Deck Builder (yes, that's the name)

Since Ellipsis hasn't been mentioned yet, here's my recommendation:

Ellipsis is an action-packed Avoid ’Em Up with minimalistic, yet powerful neon styled visuals. Guide your ship through a mysterious universe while deftly avoiding hordes of roaming enemies, spikes, lasers and more.

Ellipsis on Steam Store

Cookie Clicker

Peggle, Nubby's Number Factory, Peglin, Ballionaire

Chess.

Civ 5 and FTL would be my top suggestions. I think anything turn based is likely to be playable with just a mouse

Buy a mouse with a joystick or D-Pad on it. Or one of those 15 button mice meant for MMOs. Then you can play anything.

Balatro!

Edit: inscryption is WASD +spacebar only, if you can do that with a slight seating adjustment. It's great for planes. The post game content might be even better than the game content, haha.

Any turn based isometric. Pillars of eternity 1 & 2. Shadowrun returns/dragonfall/Hong Kong.

Here is a good one. The Case of the Golden Idol

Recently did another Plants vs. Zombies run, so I'm gonna throw this one into the mix here.

Give Kingdom of Loathing a try.

Balatro

You did say "just right hand," there was a thread before asking for one-handed games in general

Get a giant D-pad for one of your feet to use for wasd

balatro!

I actually played all of Talos Principle using only a 5 button mouse when I broke my arm a few months ago. I mapped W and S to the side buttons, jump to the middle click, and the game is actually perfectly playable with this controls.

If you don't mind something older, both Star Wars Knights of The Old Republic games can be played only with mouse. It's bit clunkier than also using a keyboard, but doable. I used to play them like that while smoking many years ago.

Into The Breach

Kinda depends on what type of games you like!

Here's a few different ones: Timberborn, Slay the Spire, Darkest Dungeon, TemTem, FTL, Into the Breach

Edit: some personal favorites too: Dungeon Clawler and Ballionaire

Vampire Survivors with arrow keys. 🧛

Oldschool runescape 😁

Slay the Spire - a roguelike deckbuilder is a lot of fun.

I haven't actually tried it, but Balatro has made a lot of waves recently and I imagine you could play that with only mouse.

Also, what kind of mouse are you using? If you're still on a no thumb buttons mouse, you should definitely upgrade. If you only have 2 thumb buttons, as is most common, I'd recommend looking at something with more. My mouse has 3 thumb buttons, and two extra index finger buttons. and while some people like that mouse (i do) some don't, so I can't say whether you'd like it, but I will say the extra buttons have allowed me to set up a lot of games that would normally require a keyboard as well into a more mouse only friendly experience.

Getting over it with Bennett Foddy.

It's a challenging but deeply emotional game. You only need to use the mouse to climb the character up.

Lots of visual novels, maybe you could try Fate?

There is unciv, a foss and free civ 5 adaptation, Humankind which was free for a time on epic games, civ 6 if it's still on sale, civ 7 if you're free to trying out new things

RimWorld would be nice but the lack of shortcuts will drive you mad

CK3 isn't as bad when you lack shortcuts, it's a fun game

https://store.steampowered.com/app/616110/SPACEPLAN/

Mini Metro was the first thing that came to mind. Fun little time waster.

Maybe some classic, more phantastical CRPGs with turn-based combat are more your juice than Disco Elysium: Baldur's Gate III, Pillars of Eternity II, Fallout. Planescape Torment, Tyranny, Pathfinder, Pillars I and the rest of the Baldur's Gate series rely on real-time combat with pause which might get tedious when only using the mouse.

Just started playing lonestar and it's been fun, Slice and dice is one of my favorites, Also pretty sure someone suggested slay the spire already but just wanna 2nd it if you haven't played it yet. Hope your recovery goes well!!

Peggle Deluxe and Peggle Nights are awesome mouse-only (except typing name i think) casual games!

https://store.steampowered.com/bundle/15495/Peggle_Pack/

For point-and-click adventures, I've enjoyed the Samorost series, Machinarium, and Botanicula!

Faster than light

I don't see any mention of the Civilization games. Civ III is my personal favorite but Civ V was also good. Keyboard shortcuts are a little bit quicker of course but it's turn based so there's no rush!

A lot of RTS games play fine with just the mouse, especially in the early stages of playing. I've seen a few mentioned but I'll put Stronghold Crusader onto the recommendation list. I generally play it without any keyboard inputs.

Every game can be mouse only with an mmo-mouse

airborn empire is a fun city builder/resource management game

With the exception of chat, try Old School RuneScape. Good game for passive gameplay as well as more intensive/focused gameplay.