Couple things. I think you are correct in that Michiru doesn't chase you in Y4, and is indeed at a bar. As the owner, I think? But I think there is at least one sub-story with her. Maybe more. It's been a while, and I couldn't find any definitive answers. Also, in doing some research on this, I found a few more....questionable elements. I almost wonder if Sega will change a few things up for the remasters of 3 and 4. Some of the content is even more dicey than I remembered.
I didn't quite finish Yakuza 4 though, but I did get to the final showdown. Had a few side quests I wanted to take care of first, so it's possible Michiru was involved in one of them.