I'm currently replaying the PC version 4.0 and have cleared the Retro's Time Challenge up to World 2! It's so much fun!
After clearing World 2-3, I tried to play World 2-Ex, but the stage info showed the score and time from 2-1 for some reason. However, after entering and exiting the stage once, the correct info was displayed.
It might be a small detail, but I'm reporting it just in case, meow~! 🐈️
↑ Before clearing
↓ After clearing