@degenerateafro
As you said he may at least has some memories from his past life, even if mostly subconscious at that point. And even if he didn't have any past memories there are plenty of kids who are 'aware' of the other sex. You can even see the change from when she first enters the bath completely naked and thinks nothing of it, but after his comment about her looking cuter she 'sees' him more as a male than just a friend- something that happens at a wide range of ages without any real 'sexual undertones,' at least for the person in question. They can get embarrassed about being seen without actually understanding why, etc.
As for biologically, even at that age some males can have... reactions, in various way. Not always of course, but it certainly can happen; I mean in general their isn't a 'hard age' (pun not intended) when sexuality 'awakens', for either sex. Medical literature has various examples and discussions around this, though its been a few years since my last classes in human sexuality/physiology/other fields that can involve this, none of which were the main field of study I was interested in. I do know there were a few cases of parents bring their kids into the doctor worried about them being sick due to being flushed, with a 'low temperature' increase (seeming like a light fever,) and breathing more heavily than normal, occasional 'tremors,' etc. - only to be told by the doctor they were having slightly sexual reactions. In a couple of the cases presented in one class it was said to generally be due to 'accidental exposure' to everyday items- like in one instance a car seat that vibrated as the car drove leading to sexual excitement long before expected. Many medical 'facts' are just generalized ideas, and there are often outliers in many ways.
As with the various daily dietary guidelines, plenty of people fall outside them obviously, and this can be the case in many different things, body temp, hormonal levels, etc.
As for the parental part, I didn't see anything that even seemed like they tried to coerce them much (other than the shared carriage ride) yet, and certainly no coercion into any sexual activities. Other than that, it wouldn't be the least bit surprising for familes who wish their children to marry to attempt to provide more opportunities for them to at least spend time together, though it's true this much... contact would be more than some older societies would consider 'normal.' And while they had 'entertained' looks through the door that doesn't mean they would have simply let her share a room had she asked ahead of time or anything like that. Anyway, I would think they may see it as more of a positive sign that they could indeed be a good match for a future marriage; many could simply see it as a sign of them having a good relationship- kinda like a sleepover, without anything sexual attached due to their young ages.
Not to mention the fact that nobility often married young; their current ages may be a bit younger than the average even for this type of thing, but even irl marriages have been arranged and gone through at ages younger than this due to various circumstances.
Not that I'm saying that it's 'morally right' or anything, but, at least from just this chapter, your comment seems to be taking things more sexualized than those involved (in the stories universe) may think. Though being a manga with ecchi of course the author plays it as more sexualized, this doesn't mean the characters themselves see it that way.
And again, not saying they should be sexualized, etc., just wanted to point out that physiological info, comparisons to 'similar' time/societal periods irl, and that, at least so far, I didn't notice the parents 'pushing' for anything sexual, let alone actually coercing them into anything.
Edit- God I need to not cast wall of text so often....
Oh and I didn't mean that to be particularly argumentative so sorry if it comes across that way.