see now this is something that's kept me up at night. because i'm pretty sure TRC's kurogane and fai are not a soul pair. and, in a way, i think that's actually kind of powerful?
CLAMP are big on fate and destiny and, as you said, they have gone on record saying many of their characters are essentially soul bonded to each other. syaoran and sakura, touya and yukito, etc. in any universe if one appears the other won't be far behind, endlessly yet unknowingly drawn to their soul's counterpart.
but i actually think this is not the case for kurogane and fai. some have speculated before that the reason these two were so powerfully drawn together in the TRC-verse was that their own universe's counterpart had already died, and while i do think that's certainly a super interesting take, i think the idea of them not being soul bonded is actually more interesting?
because it would mean they were never actually meant to be together. no cosmic force pushed them toward one another, no preexisting bond bouyed those feelings. they were simply collateral damage of someone else's destiny. only there at the right time due to a twist of fate. an aberration. an accident. somebody mucking around with what was supposed to happen. but essentially it means that everything these two did regarding each other they did on purpose. deliberately.
in a way they created their own destiny, they bent fate to their will and said no, this one is mine. when kurogane put that sword to his own flesh he defied fate. this fai, our TRC fai, was a thrice cursed child; he was always meant to die. until kurogane said actually fuck that - what do we say to the god of death? not on my fucking watch. he changed his own destiny by force. a killing machine learns that the most powerful form of love is to protect? and uses that to take fate by the throat and tell it to fuck right off? fucking sublime. he chopped his own arm off and pulled the man he loved out of destiny's cage, thereby changing his own fate by choosing fai. deliberately and without hesitation.
and fai, in choosing life, in choosing love, in choosing kurogane, in choosing to let himself be loved, in choosing the life he made over his own towering guilt, self-loathing, and despair? he changed his own fate, too.
i don't think they were ever meant to be together. but they chose to be anyway. not because of fate, but despite it. and i think that's pretty fucking rad.