Chapter 891 was definitely a controversial chapter in regards to Power Scaling and Luffy & Katakuri, but I have a reason which just might justify Luffy’s catching up.
So it has been stated that haki blooms through intense battle. Not to say that you can’t improve your haki via training like Luffy did during the timeskip, but just surviving tough battles and winning is a much greater multiplier. This is where is the difference in Katakuri and where Luffy’s improvement comes into play.
As we know, Big Mom’s territory is comprised mostly of Whole Cake Island and the dozens of other islands that make up Totto Land. While she does have territory in other Islands like Fishman Island, Totto Land takes precedence over all. This can lead us to believe that Katakuri’s conflicts with other big name pirates have been on his home turf and while he was defending his family. I really doubt that he has gone out to sea and picked fights that would prove to be as intense as the ones Luffy has. This is also supported by the fact that Katakuri has never fell on his back during battle, and I think we can all agree that if you are fighting someone equal or close to equal in strength, you will fall.
Therefore, because of the fact that Katakuri’s prowess in observation haki has bloomed through his intense training, while Luffy’s is blooming through intense battle, Luffy can catch up to Katakuri!
*Theory by thegend
