They keep teasing it! In both the anime and manga! At the very least, their relationship seems to go deeper than that of a mere bodyguard and charge.
Reincarnated!Kagerou somehow inherited parts of Soushi that reincarnated!Soushi did not.
Okay, I need a better way to put this, but there needs to be a theory on why reincarnated!Kagerou's face looks nearly identical to Soushi's
and why he's a noticeably more sensitive person this time around, despite the characteristics he did
- Um. It could be that Kagerou always looked that way, we've never really gotten the chance to see his face before then. His reincarnated self does look like how his original self did before he grew out his hair, and even back then he had a haircut that was markedly similar to Soushi's. This troper concedes though that it's likely the mangaka had an intention with drawing so much focus to Kagerou's face when she unmasked him so there could be something there.
- As for the slight differences in personality, it just could be attributed to the fact he did retain his memories and therefore is 43 years old mentally, and he has a better sense on how he should approach a situation... selectively, of course.
Kagerou and Soushi are related.
It could explain why their faces look so similar
. Plus, it seems like the families of genetic throwbacks like our main cast intermingle with each other quite a bit. It really isn't that big of a stretch to imagine.
Kagerou has a hidden case of Matchmaker Crush
on Ririchiyo, and decided to try change things in the reincarnation timeline, hence why he wrote to her there.
He's admitted in-series that he holds some regret that he didn't get to know Ririchyo the way Soushi did, which indicates he might've developed feelings for her, or at least had the potential to. But he figured that considering how enthusiastic and encouraging he'd been about Soushi writing the letters, it wasn't his place to get in between their relationship and stepped aside. But then, when he found himself reincarnated with his memories and once again engaged to Ririchiyo, he decided he wouldn't pass up the opportunity to correspond with her like he had in the past. This led to the development of actual feelings on his end which is why he seems way more invested in her and her feelings this time around.