You can see the Big Wheel on the monitor next to Drew. He's waiting backstage while they set up for the Showcase Showdowns.
(Which means that that shot in the Instagram video was taken
after the April Fools' moment, even though the video is pretending it took place beforehand.)
Also, what was so special about Drew's Studio 33 dressing room ? While he surely has needs, he doesn't strike me as a person who would need or want a "special" dressing room unles absolutely warranted.
I don't know the why of it, but instead of Drew using the dressing room that Barker (and all the other hosts who hosted shows in Studio 33) used, two of the smaller dressing rooms along an adjacent hallway were converted into one larger space for Drew.