mata has firmware included, it is installed when you update or sideload
firmware empty is called that because that repo doesn't actually contain the proprietary firmware
this is modem and bootloader and trustzone: https://gitlab.com/divested-mobile/firmware-empty/-/blob/master/mata/AndroidBoardVendor.mk
mata is not an avb/vb2.0 device, only vb1.0 as per the line on the downloads page.
only avb devices get avb keys
full means all firmware partitions and ue means update engine.