All I want to do is fly transport helicopters around in an online multiplayer scenario like I do in BF 2042 on winblows.

BattleBit Remastered
- F
- Hard to get used to but worth trying. Neck beards are squawking that it's abandonware now?
  
  Possibly. I haven’t played in a while but it was quite good when I did play.

There is a very old sim game, Simcopter, that might scratch this itch. I have no idea how you would go about obtaining a copy though.
The short version is you fly around a simcity style city as a freelance chopper pilot basically. Spotlight criminals, dump water on fires, air taxi the wealthy, etc. You get cash rewards you use for fuel and upgrades to better missions. You can even load up a simcity 2k save and play in the city you built.
- It's old enough that it's abandonware now...if you can get it to run on a modern system: https://www.myabandonware.com/game/simcopter-9zw

I haven't tested it myself to confirm it's playable on linux, but Rising Storm 2: Vietnam has exactly what you're talking about as far as helicopter transport roles.
- Nothing quite like crash landing a squad into the jungle under fire from Vietcong. Or the reverse, swooping in to grab the last three guys still alive surrounded and under heavy mortar fire

If all you want to do is fly a helicopter, try Flightgear. It's probably nothing like BF 2042 though. FlightGear is a flight simulator with focus on realism (physics wise) while Battlefield probably oversimplifies this by a lot.

Does PlanetSide 2 work on Linux?
- Sure does. There was a little jankyness but I'm not sure how much of it was due to running on linux or was just the game itself.
  
  Awesome. If there are lobbies, this is a game that tries heavily on team transport.

Battlefield has my fav heli flying. It's simple yet so skill expressive. Every casual game should have that same control.
- the mini from rust is my personal favorite

Look for footage of transport pilots in Arma 3 King of the Hill mode. They fly people into hot LZs constantly.
There are also single player transport pilot missions, some combat missions and some not.

Check out Squad, it runs well on Linux, but the game is more of a milsim like Arma, than Battlefield.
Still lots of fun though, and helicopter pilots are always welcome if they can fly the thing well (takes some practice).

Battlefield 4 still works on Linux and we always been more transport pilots...especially on Flood Zone.

Heliborne? Not played it in years now, I think another dev took over and rebuilt it for some reason and everyone hated it but the they made the original version available as well. No idea the current state of the game.
It also runs natively on Linux