Scott Manley of the YouTube has a great video that addresses the extra level of the tower, located at the seven minute mark of a recent posting.
Verbatim transcript from the video:
So pad 39A is where they launched from. An historic pad... saw the
launches of Apollo, Space Shuttle, but SpaceX took control of it in
2014 and they began modifying it for Falcon Heavy and later Crew
Dragon. And they actually took the existing static service tower that
was there, so that tower they climbed up is actually made of pieces
from the tower that was on Mobile Launcher One, which carried Apollo,
a bunch of Apollo missions, Apollo 10, Apollo 13, I think five Apollo
missions flew off that. These would be a pad which had the rocket on
it and the tower was attached to the pad to be carried by the
transporter. When they switched over to shuttle, that tower was
disassembled and segments of the tower were used to build the access
tower for the space shuttle. Now the space shuttle had it's uh, was a
different height. It had different things at different heights. Crew
access was much lower down on the space shuttle. At the very top of
the space shuttle tower there was the cap for the tank that would
continue to replenish the hydrogen and oxygen. So when SpaceX
refurbished the pad, they had to work with the existing tower
structure they had. And you'll notice that after the elevator ride up,
they have to take an extra set of stairs. The reason for that is these
segments were twenty feet, you know, six meters apart, and the height
to get into the dragon was a sort of half-level, so they added an
extra half-level, but to get that half-level, they had to take a set
of stairs to get to that half level.
The rest of the dialog is unrelated to the question about the stairs/elevator, etc.