Searching for a lag-free Notes app with auto handwriting refinement on iPad

Hi, can anyone help me please?

So ive been using notes up for my school notes and i use apple pencil it was going very good smooth and all but now that my note got big it started lagging i contacted apple support but idk we were not able to solve this issue so now im looking for new app for taking school notes WITH APPLE PENCIL but cant seem to find what exactly im looking for notes app is so nice and beautiful for real and it also has handwriting correction “auto refine handwriting” which i like it very much bc i have very ugly handwriting and if i write something i cant read it so i cant really switch to normal pen and paper SOOOO MY QUESTION can anyone suggest good app for taking notes that also has auto refine handwriting??

my notes app just started lagging for example when i write something it appears after 2-3 seconds and meanwhile ipad gets very hot like its almost burning my hand and battery dies very fast if i start using it on 100% in 5-10 minutes max its already on 65% .

yes im on latest update no its not pencils problem yes its charged and on so these are questions that apple support asked me theres nothing wrong with ipad theres nothing wrong with pencil i tried icloud i tried offline literally everything i deleted my whole study note adn created new one at first everything was fine but at the end it did same thing as it was doing before.

[Re-Titled by Moderator]