As far as i can tell the openBMC support list is quite small :/

Most vendors are indeed running Linux. For example, HPE iLO 5 is capable of starting smart storage administrator from bios, and when doing so it just launches some flavor of centos, launches SSA server then starts an antediluvian build of Firefox pointing to it.

I wouldn't be surprised to learn that the chip serving iLO was Linux too.