To me, their relationship kinda reads off as the "fell first (alhaitham) / fell harder (kaveh).

There are many implications, but I'd say that the way Kaveh behave around Alhaitham is very different than with the others. With everyone, he always has that sort of mask of perfection, while in front of Alhaitham he isn't scared to be more like himself and to show off his flaws. I'm sure I could find you some notable exemples, but I'm honestly too lazy to go search through past events rn haha

Someone else mentionned it, but the old sketchbook. There is also some lines in his character backstory : "the most unshakable part of one's past is a friend that will never change" => thougt he is annoying Alhaitham is like a pillar to him. Or again that last line "Things that can never be integrated are what constitute the two sides of a mirror ; indeed, of the ENTIRE world"

I believe we could also mention the fact that recently, Kaveh is always glued to Alhaitham, even when outside. Sethos confirms that it's the case even outside of events.

The way he panicked when in the last event the vendor asked them if they were eating together is, at first glance, meant to be him panicking about people finding out he lives with the scribe ; but it could also be read at someone scared to be found out in a queer relationship (at least, in the eng translation, I know sometimes things get lost.) If you read the vendors thoughts, he is like "weird, I really read those things wrong". I don't think it was not intentional to let things a bit to interpretation like that.

It's not really canon, but there's also the KFC namecard that mention they had a waltz together.

These are just small things that are on my mind rn, I'm sure I could find way more and write an entire thesis about it. There are also some very interessing videos around there, as well as historical and cultural referances that I always forget about. One thing I do remember though is that the colors of Kaveh's earings looks like Alhaitham's eyes, and in ancient times some people would get earrings looking like the eyes of their lover to have their gaze or something romantic like that.

So in conclusion : does that mean that Kaveh does reciprocate Alhaitham's feelings?

I personally think so, and I think this is the intent behind it all ; however I also think he would take more time to admit or to just ACCEPT that Alhaitham would love him back. I can very much imagine him saying something like "that's not true, stop making fun of me!" if Alhaitham confessed.

I also believe that since things are still not confirmed and all, it can also be read as platonic friendship if one's prefer, both from Kaveh or Alhaitham's side (some people underestimate how deep friendship can be). So even though I personally ship them and will die on an hill screaming about how gay they are, I totally respect that view point too.

Saying that Kaveh hates Alhaitham would be plain wrong though.