Also there is a potentially entirely too subtle hint at something in the Naoto section ofthe update.
I think I might want to take a crack at this. The two things of note are
1. Mato (and BRS to an even greater degree) was unsure of Naoto's gender, which is a doubt I don't believe any character expresses in P4 canon. BRS in particular seems to doubt the idea that Naoto is a "Prince".
- Relatedly, Mato seems to find Naoto 'familiar', although Mato eventually decides this is just because Naoto is a minor celebrity.
2. Naoto was staring at Mato, in a way that was described as "Intense and laser-focused, as though attempting to dissect you in that instant." From this, it's likely that Naoto either finds Mato suspicious or recognizes her in some way (possibly form the case where Yomi disappeared last year).
The possibilities people have already put forth are:
Option A: BRS ran into Naoto's shadow in the TV World. This requires the least amount of assumptions, but it also seems pretty unlikely that BRS would have run into and taken note of Naoto's shadow in particular; unless she's already been to the TV World, there shouldn't be anything to set her shadow apart from that of the thousands of other people living in Inaba.
Option B: Naoto has an Other Self and BRS has met her. This would explain BRS's reaction, but I think if this was the case we would have seen some evidence of their encounter before now, either through dreams or through invisitext (like with Yomi's Other Self). The idea that Mato is recognizing her
through BRS seems to be on the right track though, because of this line
Your eye itches slightly but you push that to the back of your mind, trying to find the thread. You've seen them before, you know they've been around…
Now, I mentioned before that it was possible that Mato and Naoto recognized each other from the investigation after Yomi disappeared, but that still leaves a lot of pieces unexplained, so I don't think that's it (and if it was that recent I would expect Mato to recognize them a lot faster). However, if I was going to make a wild guess, the possibility I want to put forth is:
Option C: Mato and Naoto went to the same elementary school. Specifically, during the time when Mato had yet to suppress her nature love of fighting (and therefore before BRS was created.) If the last time Mato saw them Naoto was still presenting as a girl, then that would explain her confusion over Naoto's gender. In turn, this would explain why Naoto was so interested in us; they were either trying to figure out why we seemed so familiar or they recognized us and were trying to determine if we still had the same bloodthirsty streak we had as a kid. Moreover, if those memories of Naoto were particularly entwined with the parts of Mato that went into creating BRS, then that would explain why BRS in particular seems to be confused about Naoto's status as a 'prince'.
This is definitely requiring a lot of assumptions, but it does manage to explain everything very neatly so I think it's worth considering at least as a possibility.