Does this game have it? Or does it play better with k&M? I don't see a joystick option in the controls menu. Thanks.

nvm

Yes it does, it has a few issues with 8-way PoV hats on some sticks but other than that it's fine. You just need to bind the thing in the options.

I don't know what 8-way PoV hats are, but I have a Thrustmaster T16000M flight pack. Will that work nicely?

It's the nipple-shaped thing on the top of the stick (and there is one on the throttle piece IIRC), other than that it should work.
Hat switches are the either 4-way (without diagonals) or 8-way (with diagonals, sometimes called PoV, or Point of View because in the old days were often used to move the camera), Everspace seems to have issues with 8-way/PoV hats but 4-way hats and normal buttons work fine and the TM 16000 flight pack (which is the pack with throttle piece and pedals, I gather...?) has plenty of buttons for Everspace already and the ministick on the throttle is ideal for 6DoF flying.

Does anyone know if joystick support works in the Linux version? I have a 6DOF controller that might be fun to fly with...

EDIT: Never mind; found the answer here (TL;DR: No).