Do I need to disable iCloud Storage Plan to change iTunes store?
Solution 1:
Well, I contacted Apple Support, and they told me this:
If you have an iCloud Storage subscription, you need to downgrade your active storage subscription to its original before you change your country or region.
So I did.
However, I am not sure if it was really necessary (because there was no red label about this in country settings like it was with Apple Music), but I didn't want to sacrifice one more month of waiting for that experiment. This is why I don't mark this answer as an accepted solution for the original question.