
It might be the rushing of the story that's making Yanu look way more certain than he is - or the manhwa just decided to skip over that part of the novel like some other bits, from what I understood. So in the end people get confused, maybe.
From the looks of it it def seems like he knows tho.
To play devil's advocate longer bc that's simply me: Yanu being so chilled out might also just be a dragon taking his time with his "ex" bc they seem fun enough and hey: kinky sex. He might be growing affection for Eyra without reflecting on it properly, hence not realizing that he's falling in love with his own mate. I'm on the fence about this take myself but it's worth a mention.

To clarify without spoilers (this is based on the novel).
In this part of the story Yanu is still 50:50 on eyra being his mate. He's is not sure if eyra is his mate or if he just enjoying eyra's companionship. (This part that got cut from the novel) in the part where yanu and eyra fight each other. Yanu said that he would destroy solath to find his mate but he would not kill eyra cause we enjoy the time they spent together so as a reward eyra will be safe but then eyra declared on that part that we would breakup from yanu and so on... and remember the part where eyra almost got k1lled by the falling boulder in their fight and yanu saves him. That makes yanu question whether he saves eyra from dy1ing(this is important cause of the dragon's mate condition) or just cause he just wants to save him not wanting to stop the fight.
There is this harsh condition on how to identify your mate which is that you can't kill them but you can physically hurt them (imprison, break their arms and legs, t0rture them) which is why being a dragon's mate is not all rainbows nad butterflies cause they can still hurt you. (There is another condition in identifying the mates but the manhwa is still not there yet so i wont say).
This is why yanu still tries to k1ll eyra after all the fightinf cause he wants to sussed eyra if he is his mate but we know that eyra is trying to stop yanu from k1lling him. And yanu is still gathering evidenc3s to prove that eyra is his mate but on this point in the story. He is just hoping for eyra that they are mates cause he enjoys how compatible they are (both in bed and out of bed)
The purpose of a dragons mate is to make them feel emotions since dragons are only born with boredom. They have mates to help them understnad and make them enjoy life and experience sadness, happiness and other emotions so that they wont go rampaging around nor k1ll themselves due to boredom and dragons are born with this knowledge that mates as essential for them for this purpose which is why mates is not limited to being lovers. I forgot if it was on this part of the story but yanu clarifies to eyra the difference between companion and lovers. Mates are much more closer to companion than a lover(this story from a dragon's perspective is not about romance its survival).

And also going back to the point of dragons hurting their mates. Some dragons do protect the areas where their mates live just so that their mates dont go dy1ng cause of monsters or anyone but that doesnt mean that they would follow whatever their mates wants(dragons are arrogant by default). Dragons DO destroy the homes of thier mates in the process of looking for them which is also some mates resent thier dragons cause dragons may accidentally k1lled their mate's family (this is kinda? Spoiler ish )
what are people wondering about when yanu 'will find out?' deadass so confused since i literally am commenting this after rereading from the start.
bc ngl im pretty sure yanus aware eyras his mate