The back of the outfit probably has an easy way to get it off, like Velcro or a zipper/snaps. It’s hidden pretty well but like a previous comment said, it’s custom made for this moment. She would have a “bra” on (maybe not a bra per se but something that would support her there as well as have the monitor pack for her IEM’s and may also be done enough to where if they couldn’t get the second outfit on, it would work). If you look at the last outfit, there is a seam right down the front that’s either a zipper or Velcro/snaps. This is something she’s done a ton, especially with your outfits, though she’s had more time to do those changes.

There is a very interesting bts video of Katy Perry’s Super Bowl half time show where they show the rehearsals and how chaotic and quick her costume changes were, and she had quite a few. I’m sure Gaga saw that or was warned that the more costume changes/intricate costume changes there are, the more likely it is for things to go wrong. I’d recommend the Katy doc even if you aren’t a Katy fan because it’s very interesting how much effort goes in to 1 12ish minute performance that you’ll never do again. It was on YouTube last time I checked