I need some easy game advices that can be played with one hand.

FTL, FTL is always the answer :D

also any turn based would work great there
my fav would be CIV, could distract you for days, and i mean days without sleep

EDIT:
forgot to mention keep talking
great fun and love, like any board-game would be.

Based on the title I was going to say eroge VNs LOL

Maybe the Jackbox party games if you want to play together? Drawful should be easy to play with one hand if she can still use a phone.

Are you specifically looking for multiplayer games? Otherwise I'd say generally point&click, VNs or story heavy indies like To The Moon would work well.

Point & Click games like Deponia. (Just one of many examples) You only need the mouse to play it, runs also on older devices and has a nice story and funny characters. Point & Click games are just not multiplayer games.

One more vote for point and click genre. There are lots of fantastic adventure games with calming, pleasant atmosphere you can lose yourself in. They also make you feel liek you are on an adventure. You wont play it together, but experience-wise nothing else is coming to my mind, that would work with a broken arm and still make anyone forget about their pain. I would recommend some classics, like The Longest Journey, Syberia, Grim Fandango, or Overclocked and Gray Matter from the 2000s. Unforgetable experiences in my opinion. Deponia is good too, and I personally love it, but its humour can be very hit or miss, and its not even consistent in game. I laughed my backhalf off on most jokes, cringed and felt uncomfortable on a few, but overall enjoyed it a lot.

Among US? it only require mouse clicking.

I think gremlins inc might be a somewhat decent game (you can usually get it cheap on kinguin or something), eventhough it is more fun with a group of people, 2v2 is possible but then you should make the game public and have strangers join. How about just a game of chess? I have been promoting this game on steamgifts lately, might fit the description. All of these games do of course require you to concentrate a bit which depending on the level of pain can be tricky.
Hearthstone might be worth a try? I do enjoy its new game modes. although its not everyone's cup of tea either I guess.
How about simply a game of AOE?

Bloons TD 6 - click link to see reason

Maybe have a look here or here

And get well soon to your sister :)

most tower defense games will do (plants vs zombies, defense grid), turn based games (shadowrun returns, banner saga, lara croft go), point and click or hidden objects (hidden through time, abc murders).

Pretty much any point-and-click adventure game or turn-based RPG; those also usually have rather low system requirements.

heres some online games you could both play togather
any of the new age of empires
Civ 3, still the best civ
most jackbox games can be played with zoom or facetime.
golf with friends
oooh sir insult simulator and hollywood roast
superfight - FREE
WAKFU - Free
Runescape - Free. played it before but its kinda meh now
tabletop simulator, EVERY BOARD GAME EVER and then some. made a few of my own

I am not sure about coop games, but as for single player, Slay the Spire will make time fly. Also, hope your sister recovers well!

boardgames with Steam versions probably would work within your constraints..

https://store.steampowered.com/app/794800/ClueCluedo_The_Classic_Mystery_Game/
https://store.steampowered.com/app/470220/UNO/
https://store.steampowered.com/app/518060/Chess_Ultra/

i hope she feels better soon.

Artifex Mundi games can be a lot of fun for the whole family

You could try any number of board game adaptations. I recently went through a Talisman obsession. Tharsis could be fun too.

I don't have much experience with it using a keyboard or mouse but Pinball fx 3 comes with 2 free tables, if the controls are adjustable to her liking, there's a lot of fun to be had there, if you're got any interest in pinball of course. The multiplayer is take turns but there's no, proper online play.

https://store.steampowered.com/app/269030/The_Yawhg/

I would play this by streaming it to her and just having her tell you what options to choose on her character's turn. It's also better with 4, so maybe you could each have 2 characters to control? Very short, very replayable.

Slay the Spire -my SO and I play Slay the Spire together all the time. One player controls the game with the mouse, and both of you can give advice and suggest strategies, and it's surprisingly entertaining to watch.

Civilization is another game you two could play together.

There's also digital boardgames like Pandemic (you can beat Covid together!), Ticket to Ride, etc.

I hope your sister has a swift recovery.

Oops, missed the do together part. LotRO and DDO are both F2P, and they both have customizable keymapping.

use remote play together to play The Yawhg and maybe We Were Here trilogy. I think child of light would also work since she can use just the mouse to control one of the characters.

I Would say TFT (Teamfight Tactic) only 1 hand u need and thats the mouse :D. Also Hearthstone ;).

Battle for Wesnoth, it's free! You can find it on Steam, too.

Man that's rough, hope she gets better soon!

100% Orange Juice or Golf With Your Friends (she just wouldn't be able to press 'c' for a freecam to get a birds eye view but it's not needed).

Check out the Alaware games. They are cute and are played with a mouse.