How to determine file system type reliably under Linux?

vfat is only to represent that it's a FAT partition, according to the partition table and fstab. fdisk -l will tell you the same thing as df -T or mount.

I wouldn't use stat, I would use file /dev/sda2 or parted /dev/sda -l to get a better idea.

Side note: fuseblk is used for auto-mounted media. There is a clear difference between the /boot/efi and the /media/... example you showed.