The game says the storage is full (or almost full) and won't let you start a level or download packs form the marketplace when there is free space on the system memory or SD card.

For example my brother's switch sometimes has the problem and he needs to delete some stuff to continue playing, but he has over 100 Gigabytes free on the SD card and almost 3 on the system memory.

I don't know if there's some kind of cache with a preset size or something, but if there is, It should be dynamically sized so it can increase and decrease in size as required