My suggestions are:

Cubirds A simple card game about collecting different types of birds. Easy to learn, quick setup, and simple scoring rules.

Fantasy Realms Another card game there you try to collect the best set of 7 cards. A little bit intimidating at first for some players because of the fantasy theme, I found that it works great with all kind of people. The scoring is quite complicated, but there is an app that can scan the cards and calculates the results for each player.

In an entirely different direction, Just One is a great word-guessing game that very easily supports different people round-by-round.

• Scout adds a clever twist to the shedding game formula, supports 3-5 players and thanks to tokens you don’t need to write anything down. But you could also just play individual hands without scoring (which I assume you’re doing in rummikub)
• eXplorers is a 20 minutes, 1-4 players, flip and write exploration game. If you don’t mind the waste and would prefer a faster setup you could print a specific arrangement on normal paper and just hand those sheets out.
• if noise isn’t an issue Ligretto Dice is a quick hoot for up to 4 players. You would need something to score unless you just play individual rounds which each will have a winner.
• Pickomino is a staple filler in our group. Funny push your luck Yhatzee style game.
• Cheating Moth would again be one that could be played in individual hands. Another shedding game but cheating is officially allowed! Getting caught is what gets you into trouble
• In a bind / yogi is a card based dexterity game for pretty much any number of players. you draw a card and follow a instruction like “one finger touching neck” or “hands touching”. Anyone who stops following even just one of their instructions is out. Last man standing wins.

I haven’t seen Skull mentioned yet.

https://boardgamegeek.com/boardgame/92415/skull

Plays well at a variety of player counts. Easy to teach. The game has a nice tension to it.

There is the problem of players being eliminated. Some people just really hate that. I’ve found that the game is short enough and interesting enough that it never feels bad to be eliminated, but your crew might not agree.

Love Letter. A very quick game with just 13 cards. Games take about 3 minutes so you can play multiple rounds if you want. Suits 2-6 players (best at max 4 in my experience). Generally very popular and easy to learn.

Comes in dozens of themes as well, if you don’t like the “princess in a castle” theme. You can find Batman, Cuthulu, The Hobbit, versions depending on your preference.

the card game “set”
https://en.wikipedia.org/wiki/Set_(card_game)

Las Vegas or it’s (modified) rerelease Las Vegas Royals by Rüdiger Dorn.

Splendor by Marc André

Nimm 6! Works great with random people. Tuto and its variants are fun as well. Kinda depends on the amount of players tho. I think that the bang dice game is fun, but more difficult. Someone on there recommend me Knucklebones.org the KutL mini game.

Honorary mention goes to Cockroach Poker. Easy and very fun. Great to learn who’s around you as well

I’ve had a lot of success with Mantis. Very easy to learn and just watching a few turns is enough for someone to understand how to play. It’s cutthroat enough that keeps players engaged, and a good balance of skill and luck so that anyone can win. Rounds only last about 5-10 minutes depending on how fast turns are taken. The components is just a deck of cards, but does need some table space to spread different cards out so everyone can see

Games I might class similar to rummikub are Upwords and Quiddler (although both are word forming games)

King Domino is a tile laying game that makes me think of Rummikub. The tiles use landscape regions to score that you select each round and try to lay out in a grid to form a “kingdom”. Each tile connects with other tiles to make regions that score for size.

Have a look at Qwixx perhaps.

I once saw Spaceteam. It’s a co-op game in an app, and I’d be really down to playing this with people but I never got to it. It seems like pure chaos, but a lot of fun.

Android: https://play.google.com/store/apps/details?id=com.sleepingbeastgames.spaceteam

• One of the variants of Love Letter. I’ve only played the Marvel/Thanos one, but it’s quick and easy enough to set up and play.
• One of the Mint games such as Mint Works
• Look at the Button Shy series of games