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You can try Steam Library Filters, but I don't think mouse only is a tag on many games.

Edit: I just filtered my library by Mouse Only and it only showed six games, and I know of many more than that can be played with mouse only.

Anything Point-n-Click will be mouse-only:
http://store.steampowered.com/tags/en/Point%20%26%20Click/

https://github.com/Depressurizer/Depressurizer

I've done a quick lookup of the games we have in common, and here are a couple of games that can easily be played with 1 hand.

Card/Board Games:
FreeCell Quest
Talisman
Card City Nights
SolForge

Puzzles:
Lyne
The Room
Tengami
World of Goo
Human Resource Machine

Action Games:
VVVVVV

Casual Games:
Kingdom - Classic
Kingdom - New Lands
10000000

Clickers:
Plantera

Point and Click Adventures:
Lumino City
Richard & Alice
Puzzle Agent
Sam & Max
The Warlock of Firetop Mountain

Social:
Town of Salem

Bonus:
Epistory - It's beautifully presented, and even though it is a typing game, it adapts to your speed, so you can play it with a single hand to challenge yourself.

i look your lib from steamdb, and found some that interesting

try board game called 100% orange juice
its only using mouse and addicted, trust me xD

board game like Knight of Pen and Paper +1 also interesting and its using mouse only

puzzle game like Lume, Lumino city and Kami also interesting and using mouse only

how about Tap Heroes ? its using mouse only and you already play it a lot xD

Since you already got many recommendations, I just leave this here: get better soon! :)

Already some nice recommendations here. A couple more that can entertain you for hours, if you like them:

• one finger death punch - great action game that can be played only with the mouse
• crusader kings 2 - grand strategy game set in medieval times Europe. It's pausable real-time so it can be played only with one hand.

Hope you get well soon :)

By hand like a crazy person one by one xD
... Yeah o_o So now I know if I go to puzzle, clicker/idle games or point and click or hidden object I have the most chance to find a mouse only game.
It took a lot of time and I still have a lot of sorting to do but depending on the feeling of what to poke it's a easy find in the end.
77 catogories and counting T_T

View attached image.

thx ducky for making this thread since its something I have been wondering a long time, bump and <3.

As someone pointed out (^^) Point and Click games definitely. Plus there is always a good reason to play those. Look at everything made/published by Wadjet Eye Games.
Also, cRPG should work for you. Divinity OS are turned based as well. Games like Pillar of Eternity as an active pause for fight (you might want to use the space bar to pause the game, but if you really can't you can either click on the UI or bind a mouse button I believe).

Get well soon!
And I don't have anything to add that isn't already said about the sorting.

https://www.lorenzostanco.com/lab/steam/u/Duckiedoodle
There's a "mouse only" tag that shows twenty-something games from your lib - obviously not a complete list, but something for a start.

Some mouse only games are harder though like Pillars of Eternity so you might want to check fully. I mean technically it isn't mouse only since you can use the keyboard too but you don't need to at all.

Grey Cubes, Bad Caterpillar, anything by Artifex Mundi