At least Steph technically isn't in a costume, though she took a cue from Bruce and made a simple domino to accompany the hood and cape. She misses her Spoiler costume, the full face covering would be a relief right now in such a strange place, and she wonders if she should cut her hair again, to make it easier to hide.

She also probably shouldn't have shown her face all over the network, but it's too late to take it back.

It's clear that Steph hasn't noticed anyone watching her, and it's also clear that her movements are purposeful, that they're following a pattern. She'd started at the edge of the sector, and has been making her way in a spiral, gradually circling inwards, though occasionally she stops on a rooftop, taking a break and a chance to look around and get her bearings.