Looking back on different character encounters and fights, I think Luffy is very close to being Admiral level, and I think he has been for a while.
In the arcs before Dressrosa we really can’t estimate Luffy’s strength. He never had to go all out and in the few moments he struggled, it was because of unexpected disadvantages in environment and such. Up until Dressrosa, I don’t think Luffy grew that much.
When Doflamingo met Aokiji at Punk Hazard, he wanted to avoid the fight. He said something like “I don’t have time to fight you right now”. He definitely did not want to fight but he didn’t seem panicked either. It just seemed like it would be an annoying hindrance to him.
What I took away from that encounter, was that Aokiji is stronger than Doflamingo but not by much. On Dressrosa Doflamingo also mentions “getting rid of Fujitora”, which he admits would be difficult but he is confident in his ability to do so.
Luffy then fought Doflamingo and won but just barely and with help from Law. I think before/during their fight, Luffy was weaker than Doflamingo but due to being pushed, after Luffy’s recovery, he became as strong as (or a little bit stronger than) Doflamingo. Enough to take on an Admiral and fight for a long time. He was probably right between Doflamingo and Aokiji.
During their escape Luffy ran into Fujitora and was prepared to fight him. I don’t necessarily think he would have won. Probably not. But he would definitely have put up a fight.
I think his fight with Cracker and everything he went through on Whole Cake Island was the final push that put him on Admiral level or very very close to. This progression really doesn’t seem unreasonable to me.
And I would say that Yonko Commanders and Admirals are around the same level. We’ve seen them go against each other before. Ace briefly fought Akainu and Aokiji. Marco took attacks from Kizaru and Aokiji. If we put Dragon on the same level as a Yonko, then that makes Sabo a Commander and he fought Fujitora. Maybe some Admirals are stronger than some Yonko Commanders and the other way around but it’s close enough, that if you’ve fought an Admiral, you can fight a Yonko Commander.
I believe all of this puts Luffy on a level at which he can fight Katakuri and win without it being a total ass-pull as many people are saying.
*Theory by Hallager98