Is the elevator door left open?

May be. I can't go up there, bc I didn't take the stairs key, so I'm literally stuck in the first segment of Turnip Hill :)
Fast replaying has its issues...

How did you came down then?

By falling.

Can I restart the level without loosing the progress (in spot repairing and photos)? The thing is it autosaved me near the lift twice and I will have to start everything as in the new game chapter start.

Yes, you can.

Like through the console?

You could also write to console:
'sv_cheats 1'
'noclip'
fly to the upper floor, and then again 'noclip' and 'sv_cheats 0', and then save and restart game.

Yeah, I know the noclip thing, just wondered if there's any other way. Thanks.

Has this been classified as a bug? If not, it should be, since it's a result of bad design, making it possible for the player to get stuck in a situation they can't get out of other than cheating or losing progress. The lift should simply ignore door status if responding to a call button.

And, by the way, as I recall, there's no door on the uppermost floor and yet the lift will work there without the door closed, but not elsewhere, so what's the point of all this close the door thing? It doesn't make any difference, and it's just added annoyance having to close it all the time... On top of being a potential game breaker.

That elevator has now been fixed in the upcoming patch.

When is that patch planned to be released?

I have the same issue, only that I have the stairs key. However, it doesn't unlock the fourth floor gate, so I still can't get to the elevator. That seems like a separate error to me.