Network booting is supported. I don't know if the architecture is similar enough to the x86 bios loading network card option roms that one could say the "ethernet controller supports" it. Booting on ARM is different.

https://www.raspberrypi.org/documentation/hardware/raspberry...

This blog post[0], says that it's not yet supported by the RPi 4, but that it's coming in a future firmware ugprade.

[0] https://blog.mythic-beasts.com/2019/06/22/raspberry-pi-on-ra...

There are u-boot forks that support RPi ethernet. https://elinux.org/RPi_U-Boot

yes. rpi3 could do it, 2 with bootloader on sd card.