@BattleFranky69:
May have been a bad translation but I interpreted it as being knocked down, not just laying down, that would mar his reputation.
Brûlée was definitely talking about about Katakuri's back NEVER touching the ground, because she goes on to say how Katakuri immediately stood up after he was born. She also describes him as always dignified, calm, strong, etc.
https://jaiminisbox.com/reader/read/one-piece-2/en/0/882/page/4
This exact speech is written over when Katakuri's true personally is revealed, to drive home the point that what Brûlée and the rest of the Charottle believe their "perfect" big brother to be like is just an act he puts on in front of them, and what he is in the dark is a self-indulgent glutton that doesn't have any issue with laying down.
I didn't think he'd necessarily take his anger out on his actual siblings (without permission from Mama, LOL)
From what we've seen, Katakuri does seem to actually care for his siblings. I don't believe he would get angry at them for any reason except possibly discovering his secret. Even besides that, nothing we have seen from Katakuri before depicts him as the type of person that would have an issue with outside assistance. What's irked him the most up until now (other than the reveal, of course) has been Luffy's resilience and growth.
but he would potentially repair the damage that last attack caused to Luffy, in a Ichigo vs Grimmjow kind of way.
The difference here is that Grimmjow wanted to beat Ichigo at his best because he wanted to prove he was better than him. Or something along those lines. I haven't touched Bleach in a loooong time, so I'm not certain it was exactly that, but the specifics don't matter because whatever the reason, Grimmjow honestly wanted to beat Ichigo fair and square. He wasn't doing it to get promoted by Aizen or respect from the other hollows, he was doing it for himself and was invested in getting his final one v. one because Kubo due to his own feelings about Ichigo. On the other hand, Katakuri hasn't shown any enemy respect or personal interest for Luffy up to this point, and was perfectly alright with winning by trapping Luffy under some mochi until
he suffocated, which is not how "worthy opponents" generally are treated.
Otherwise I really don't see how Luffy's getting back up after.
The last few panels could be a future vision, as some people have already said. Or Luffy could simply "willpower" his way through the rest of the fight (it's not like his vitals were hit) until he can get back to his crew. This is a shounen manga, after all. Katakuri suddenly going from being worried about Luffy's growth to giving him a second chance to fight is not the only way for the story to proceed.
He might even be intrigued by how Luffy's seemingly rapid advancement progressed and want to test his mettle just for kicks, like "You wanted to beat me at my fullest…and you're clearly advancing at a rate even I didn't anticipate. Let's settle this properly, from the beginning, and see who is truly superior." Surely an awakened DF user can fudge with his ability and make some skin grafts or whatever.
On the second to last page of this chapter, Katakuri is clearly worried about how Luffy is approaching his level of CoO and wants to kill him quickly to prevent that, so it would be a bit jarring if he suddenly did a 180 like that.
But if this level of injury is what it takes to trigger Luffy's awakening, that would be even more satisfying.
That's a cool idea and another possibility for how things could go without needing Katakuri to patch Luffy up.