The magic in all of that is
@LightBulbFun digging up and properly getting all the kexts together to make it work on a computer with PCI graphics.
All PowerMac G3s, including the beige series(desktop, minitower, AIO) and the B&W had socketed CPUs. They work just like an x86 socket from the era like you'd find on a Pentium-left a lever, pull the old CPU out, and drop the new one in. G4s that fit this socket are plentiful since Apple made them(Yikes! G4) and there were bunches of aftermarket ones from ~400mhz all the way up to 1ghz. On the B&W, you have to flash the firmware as Apple locked out stock ones from booting a G4, but otherwise it just takes some tinkering to get the L2 and L3 cache to work properly. Sonnet and others packaged all of this up nicely back in the day since they sold them commercially.
The real issue is that the on-board ATA controller on beige systems is...quirky...to put it mildly and unless you can squeeze Leopard into 8gb(doable, but barely) you need a bootable ATA or SATA card. They're out there, and at least the ATA ones were reasonably common back in the day because of the limitations of the onboard controller. A USB/FW card is also a good idea, and a better video card(Radeon at the minimum, preferably a Radeon 9200) is a good idea than using the onboard GPU.