According to the new One Piece Vivre Card Databook, it seems that Sanji can use the power of Observation Haki to “see the future.” The image used depicts Sanji dodging Katakuri’s attack.
Here the translation: “By reading the movement of signs and emotions, you can grasp the surrounding situation and avoid danger. Some people see the future a little ahead due to extraordinary discipline.”
Future Sight is perfect for Sanji because he’s collective and calm. But if there were different applications of Advanced Observation Haki (so far, there are only 2: precognition and sensory types), I can see Sanji having the “timestop” sorta type of Advenced Observation Haki where he can slow down the perception of time and controls his brain to think faster and act quickly.
Examples of that is when he saves Chiffon from Oven in Whole Cake Island and when he saves Chopper from Queen in Onigashima.
And then there might be another type of Advanced Observation Haki where you can hide your presence in your surrounding. Example would be Lafitte infiltrating Mary Geoise without the guards noticing him. Even Mihawk couldn’t sense Lafitte was there. My prediction is that Sanji will have all fours types of Observation Haki that I listed above.
Finally, let’s not forget that in Chapter 998, we see Luffy and Jinbe never sensed what Sanji did and Luffy implied if his Observation Haki was better he would’ve sensed something.