I mean, he beat the shit out of him. And then Katakuri drops "Will you defeat Bigmom soon??" and then they both smile iirc. But this didn't seem to have gone deeply enough to the point of being friends YET ? Maybe it'll happen, but their bond wasn't formed.
That's true. Katakuri was minding his own business dealing with Goofy in the mirror-verse. Maybe he'll ask Luffy beyond his status as a Charlotte sibling.
But Elbaf first ! And maybe Teach vs Luffy will go down as soon as the next arc