rpi-update is unique to Raspberry Pi OS and it's compatible derivatives. The only way your going to get new "firmware" is by installing a newer LE image as they are baked into the image, or downloading and installing them manually to /flash.
The files you are talking about are baked into the image by the bcm2835-bootloader package, see here. They are installed to /flash on upgrades by this script. I believe the tar ball (hosted on LE's site) is prepared by this script.
The situation is by the way the same for the EEPROM firmware, so if you have a recently purchase RPi4 and installed LE 9.2.8 then yeah rpi-eeprom-update is going to only have older EEPROM firmwares available for installation, like the bootloader those are also baked into the image and are only delivered by LE image updates. You can manually download those and install them with rpi-eeprom-update command line switches, or pop in a recent RPiOS and burn in the EEPROM firmware that way. But the bootloader files are loaded from the SD card/disk by the EEPROM, they are not burned into a ROM.