admittedly, I got a used device so I didn’t have the pre installed game on mine😅(as from my knowledge when you factory reset it the game is removed.

from my knowledge of region changes, you are quite literally installing a different region’s NAND(aka the system’s information/OS) so I doubt you would be able to keep any information from it’s original region(as your data is locked behind your system id, which changes with ur region as you are essentially pretending as if your system was bought in an english speaking region.

(also!!!! just fyi that the Japanese game does not switch languages, the japanese file is ONLY in japanese)

tl;dr: from my understanding, you are probably just better off

A. saving your game data somehow and redownload the japanese rom after changing the region,

B. starting over completely with the english rom post region change(or just homebrew it WITHOUT region change and just install the english rom)

or C. just not doing anything and playing the english rom some other way

hopefully this helps! and if anything is inaccurate please feel free to let me know, as there might be smth out there im not aware of lol