So this explanation won't be as long. But in short some things remain the same as with the Adepti and yokai but there's very key differences Zhongli mentions but Baizhu hinted at and Xiao experienced.
The Courtship & Claim
The first difference is due to yakshas all having predatory illuminated beast true forms such as Xiao's Vermillion Bird form, their instincts are extremely strong and can even be aggressive. The adepti and yokai think no yaksha has ever preformed this rite...this is in fact false. It has happened but it was never with mortals and only ever in secret within their tribes. They are extremely sacred to them as unlike some races yakshas only ever take one mate and it's always their soul mate. The yakshas call it something completely different in fact: Soul Bond.
Soul Bonds go far beyond the 3 steps of Courtship Rite and will most assuredly trigger a great deal of agony for the one who triggers the ceremony. They are very often confused for the same thing. Like the yokai and adepti it starts with the 3 stages from Courtship Rite and uses pretty much the same ritual. But that's where the similarities end. Unlike the adepti and yokai and other elementals, the mate's mark of the intended begins to fade after they have the third step completed. This begins to trigger what yokai and adepti mistake for a rebound which can be extremely painful. Xiao was too young unfortunately to know this, having been a slave for a long time before Zhongli rescued him. And his tribe died out before he could learn properly. Otherwise the other yakshas would have taught him Yaksha Health Class 101. lol
Baizhu however knew instructing Lumine to do what she did. The Soul Bond phase causes a great deal of agony as I mentioned, it feels like your body got dunked in magma that's the best way I can describe it(ouch...that'll hurt). Their instincts get extremely strong and they become far too dangerous to approach safely once their eyes, markings, and hair change color. This is why everyone and Paimon were instructed to stay away. There's only two things their primal side desires once in this state or it begins to take hold.
The desire to mate and destroy anything that they see as a threat to that mate before the Soul Mark is placed, their souls "bound together" and mating completed. The mark acts as a bounding of souls, making it easer to track where they are between both mates, letting them know if they are near or far away(not exact location its like a game of hot'n cold). The ability to be empathic to each other's emotions remains the same like with the adepti and yokai. The soul bond is something not common knowledge outside the yakshas so how did Baizhu learn it in Xiaolumi's Book 3? Who dare say how he learned it? Only time will tell. But the fact remains while Xiao didn't know much on the Soul Bond due to his age his instincts did and were what guided him. I should mention if the intended at any time turns out to be in "heat/rut" this ups the aggression to threats and the yaksha in question grows anxious and restless. Which is very apparent during late spring and autumn every couple 10 to 100 years. Hopefully this explain things and cleared some questions.
The Soul Bond
The yaksha race do not take "weak" mates, they are very finicky and picky since they are considered to be a "Monogamous" species of Elemental Race. They only ever take a single mate throughout their incredibly long lifespans. The instant they claim their mate for the final time, they bind their souls together to the point they can be considered a single entity in a way. This is a double edge sword however as if one mate dies the other will soon follow as the loss of their other half is just too painful to be without.
Even out of mating season the pair will often mate, strengthening the soul bond. Eventually it reaches a point where they can share each other's damage taken in battle and even sense their conditions. This is due to how the Soul Bond Axis works. The Soul Bond Axis is often described to be like an invisible thread tying the mated pair together. It'll even let their partner know when the other goes into heat or rut, essentially effecting the other in turn. Which will drive the mated pair to mate until this primal need is sedated. Breeding seasons tend to be in spring and autumn for mated pairs. With cubs being born during the rainy seasons of Sumeru & Natlan. Another fascinating thing many do not know is mated pairs are capable of sharing each other's mindscape and dreams.