A “ROM” of this menu is a binary file extracted from the DS’s internal (firmware chip), not from a game cartridge.

Even on modern Nintendo hardware:

The term "Nintendo DS menu ROM" refers broadly to the firmware and menu software that runs on Nintendo DS-family handhelds (original DS, DS Lite, DSi, DSi XL, and later 3DS family variants when running DS-mode). This discourse examines what the menu ROM is, its architecture and components, how it interacts with hardware and cartridges, the role it played in the user experience and homebrew scene, the security and intellectual-property implications, and its legacy for preservation and modding.