> Is there any example program that actually runs on the rpi gpu?

ThreadX.

https://en.wikipedia.org/wiki/ThreadX#Products_using_ThreadX

This RTOS, later rebranded Microsoft Azure RTOS, later still made FOSS:

https://www.theregister.com/2023/11/28/microsoft_opens_sourc...

ThreadX is the RasPi firmware. The GPU is the primary processor of the Pi: the ARM cores are essentially just co-processors.