Maybe he had a rough day at work and decided to peek in on her sleeping to remind himself What He Fights For (which unfortunately backfired horribly). Or something like that. There are ways.

Yeah, the activated driver made it kind of obvious that he either was Zangetsu or was in charge of Zangetsu. And he knows Michi's smart.

I imagine trying to warn Kouta/the team while not tipping her hand will be just as effective as it is in canon. Do the Yggdrasil records note her relationships with team members at all? I would think not in a huge amount of depth if at all.