One Handed Games?

It's not what you asked for, but you can use a software to control with your voice what you can not control with your thumb anymore (and therefore you can play almost any game): https://switchgaming.blogspot.com/2019/06/mishkinamish-voice-control.html

I think This War of Mine and Beholder both can be played with only a mouse and both are great games.

fap time? xD

Sid Meier's Pirates!!
n_n

When I broke my hand I played Puzzle Agent and Cossacks, so I recommend those
Eschalon series comes to my mind which would be good too, many of the RTS games, railshooters and all the hidden object games you can find are playable with only a mouse

Many turn based strategies and games like Papers Please or Do Not Feed The Monkeys

If you're into turn based strategy, I used to play Civilization V a lot one handed. Keyboard shortcuts help a little to speed up gameplay but you can easily play just with your mouse hand.

A lot of turn based games can be played with only one hand.

Oh and of cause visual novels + point+click advnetures.

Heroes of might and magic(Any of them)
sid meier's civilization
Crusader Kinds 2
This war of mine
Most visual novels
Dungeon of the endless
Slay the spire
The flame in the flood
Northgard
Party hard
Stronghold crusader 2
Tropic(Any)
Oxygen not included
Rimworld

Koloro

Here's a previous thread that may help you find some more games: https://www.steamgifts.com/discussion/rJnVK/what-are-your-favorite-games-that-can-be-played-one-handed

Plague Inc: Evolved

Here is a few months-old thread that may help you in your quest: What are your favorite games that can be played one-handed?. Unfortunately hand accidents are more common than one would like.

You'll find lots of great recommendations there. Hope you get well soon!

EDIT: Ninja'd by the quicker AllTracTurbo ^^

one finger death punch and it's sequel are both really fun and only require lmb and rmb.

Had the same problem in summer: Slay The Spire, For The King, Renowned Explorers, FTL, Darkest Dungeon, Divinity Original Sin 2,
Plague Inc Evolved, Wasteland 2, One Finger Death Punch, Papers, Please, Thronebreaker, Baba is You

Pretty much any visual novel or point & click adventure game would do ya. Here's a few others . . .

60 Seconds! Reatomized - While the Scavenge section does require using the keyboard, you can play the Survival part by itself, and it uses just the mouse.
Eets Munchies - It's been a while since I've played it, but I'm about 99% sure it can be played mouse-only.
Faerie Solitaire Remastered - There are very few solitaire games I would recommend to folks, but this is top of the list.
Fallout Shelter - Two advantages it has over Fallout 76 is that it can be played mouse-only, and it's free.
One Finger Death Punch and One Finger Death Punch 2 - The most fun you can have using only the right and left mouse buttons.
The Room and its sequels - Puzzles for hours!
Zafehouse: Diaries - In fact, I'm pretty sure all the Screwfly games can be played mouse-only.

If you like SHUMPs, DEEP SAPCE WAIFU has a one handed mode in all their games. ( ͡° ͜ʖ ͡°)

any turn-based game, isometric RPGs, many adventure games, "slow" puzzle games. Pretty much anything without a lot of action

I played (and maxed out all achievements) this when I've got broken finger bone once. I'm righthanded, but I've played with only left: https://store.steampowered.com/app/325090/Deep_Dungeons_of_Doom/

Darkest Dungeon

That you can play with Mouse, one handed.

Chicken Invader Series. :D
Raptor: Call of Shadows if i remember right. ;-)
Any Hidden Object Games
Visual Novel Games
The Settler Series
Empire Earth Series
The Patrician
Anno Games
SWINE

And there are much more i guess. So dont worry buddy and get well soon. ^^

both Montaro and Montaro: RE if you like constant runners.
Darkest Dungeon for turn-based roguelike.
Planescape: Torment is a crpg that can be played with just the mouse iirc. Shadowrun games can be mouse-only also.

was gonna suggest the Telltale games but then i remembered the damn QTEs and sometimes walking portions that plague even the best ones, so that's right out, lol.

i hope your recovery goes well!