Is there any way of directly repairing power armor without first having the companion exit it, then the character enter it to place it in a station, then repair it, then enter it to move it out of station, then exit it to have companion re-enter?

Yes - Go into trade with them, take all their power armor plates. This will leave them still wearing the frame. You can then repair their plates while you repair your power armor. Then go into trade again and give them/equip the repaired plates.

Doesn't work, because if there's no power armor in the station, it won't repair anything, so companion has to leave his.

Anyway strange that only power armor require repairs.

there has to be power armor in the power armor station for it to work, which that shouldn't be an issue because you can get 2-3 power armors early in the game. otherwise buy a power armor frame and that will work as explained to you by the other guy

Also, if you have them exit their power armor near a repair station where you don't already have a suit, you don't actually have to get into it and move it. Activate the repair station and the closest suit of power armor should automatically move to it. I don't see why you can't order them back into their power armor while it's sitting in the station ... though I admit I haven't actually tried.

This. I park the suit from the Museum of Freedom in the Power Armor station and leave it there, so I always have a suit there to work on.

The robot detective couldn't enter it at sanctuary while stationed, but maybe it is because the station is parked along a wall, maybe it has to be moved out from the wall in the open; still the character sort of teleport behind it when entering. They should patch it.

Also companion won't receive all armor, it says he can't carry anymore even if the ones received are equipped. So he got to exit and reenter it.