Literal dictionary definition of a BIOS:

Image

Note the part regarding enabling a computer to start the OS. But regardless, this point is largely moot as we are just arguing semantics.

No the PS4 doesn’t run a PC-style AMI/Phoenix BIOS, but instead a secure chain of Boot ROM to bootloaders - however, so do Macs, which are PCs.

Dumps of these console boot ROMs and loaders - at least in emulation circles - tend to be colloquially referred to as a BIOS, as it constitutes a System that handles Basic Input and Output.

It even putting this one point aside, it runs an AMD-designed x86-64 APU, that was available to purchase for PCs (AM1 socket) albeit with a reduced power GPU.

It runs GDDR5 unified memory like a modern iMac, or Steam Deck.

It natively runs a UNIX-derived OS, again like an iMac, or Linux on the Steam Deck.

Let’s just face facts, the PS4 & 5 are just iMacs in drag 😉