I was going to claim panel one was revenge for all the times American's have been generalized as cowboys and/or Texans, but then I remembered all the bad British accents in Hollywood movies and just American-made media in general.
Have all the Americans as cowboys you want, friends across the pond. We deserve it.
Before anyone accuses me of being an evil tease, I genuinely really like this approach to this situation. Instead of awkward camera angles and Austin Powers style covering up, Sarah's in plain view, we get a variety of outfits, and poses like the one in panel three just wouldn't happen or be heavily obscured otherwise. Now she can just do whatever with the added context that those outfits aren't really there.
As Nanase says, this test was about ego, pride, teamwork, and trust.
For example, Nanase might not have been thinking clearly, but she still knew how she felt about Sarah. If Nanase didn't trust Sarah, she might not have done as Sarah said.
As for Sarah, If she had a big head about herself, she might not have realized she was the final "block", or removed the handkerchief.
Ultimately, the puzzle wasn't about outsmarting the puzzle. It was about whether they could work together to get it done under those circumstances.
Which all paints the dungeon is a somewhat more noble light than is implied by Nanase retaining that form and being left in just a swimsuit.