According to the Ledger Developer Portal source you shared, the firmware is in the secure element chip, not the MCU.
There is firmware on both, but the firmware updates you install via Ledger Live predominantly target the MCU. The errors you get with an outdated device are either "MCU firmware is outdated" or "MCU firmware is not genuine".
According to [1], Ledger uses ST MCUs with flash memory in the 16-32 Kilobyte range. So I highly doubt that much of the firmware is stored directly on the chip.
The secure element actually has much more storage, 320KB to be exact; so it's likely that much of the firmware is in the secure chip.
This all doesn't really matter, though. The fact of the matter is that as soon as you install firmware with seed extraction capability, it's game over for your privacy and security.
[1]
https://blog.gridplus.io/hardware-wallet-vulnerabilities-f20688361b88?gi=205af29b0222