I doubt they are using exFAT in their internal memory. Why would we need to install the exFAT update if it would be using exFAT internally already?
They are presumably using their own Filesystem
EDIT: They are apparently using FAT32 internally:
https://switchbrew.org/wiki/Flash_Filesystem
Do you just assume that they can or do you have any documentation on this? Maybe you can provide patches to the homebrew developers, then.
my bad , have done some verification and your right default file system is fat