I don't think Sids knows it her. I think is more that, she reminds him of his first love, Qatra, her first life. We weren't given any hints that reincarnation is normal, so he has no reason to suspect that a girl born 100 years after, to be her. Plus the 'Pillar of Light' (what gives a long life) is in the capital of the empire and we currently to the south, in the neighboring Olwen Kingdom (ch1). Presumably they have a normal life span here, and her Uncle can vouch to her birth too. Having Sid go "OMG It's Her!!" is far-fetched to me.
And that face Sid made at the end look like a "...gh. Be still ...my Boner" face.
I'm wanting for the MC's 'oh shit, may as well come clean' moment. I kind of what to see something like:
*Salute*
"Qatra reporting for duty, your Majesty."
"I have returned" (*I can't be the only one, who only hears this line as a Dragoon, right?)
Followed by a super embarrassing story from his Majesty's youth.