Klingon Facility Away Team
The outer door of the airlock is already open. This facility was set up with a specific protocol in mind... i.e. there is no docking provision, just access. It's an airless asteroid, so unless all personnel were expected to wear spacesuits just to go from the ship to the base, this is the most logical way to do it.
The old Federation ship is a different prospect. It's not close enough for the air envelope to reach it, so, presumably, one would need a spacesuit to reach it. On the other hand, why wouldn't it have been parked closer?
Silviene reaches the airlock without any difficulty, pretty much just flying across the distance in the near-zero gravity. She enters the open airlock with only a slight glitch--she stumbles into the sudden one-gravity of the facility, barely managing to keep her feet at the abrupt change.
Those in the shuttle can see what happens, and since Silviene is standing and not floating, it's a good bet there's artificial gravity in the facility.
After a full minute of waiting, the outer door remains open, and the air tunnel is still in place.
As with normal airlocks, the inner door won't open until the outer one is closed. Normally, that occurs when there is air pressurization in the airlock equal to the interior. That should be the case here, but Silviene can't get the inner door to open. It's probably just an extra security measure, in case the air tunnel collapses.