For me, the Raspberry Pi comes close. It's a limited machine, the specs are the same for everyone with your model and there's plenty of scope to make it do impossible things if you apply yourself.

Is the hardware of the Raspberry Pi really fully documented? The GPU too? How about WIFI chips?

I've tried several times to make a tiny kernel for x86, but always feel it's either too old interfaces like the PIC, TIMER, VGA, IDE etc, or chip specific. I can't give my friend a bootable USB because he/she might have a different hardware setup.

Everything that's needed to make an OS is documented, either directly or (like USB) in the Linux kernel's source code. Even the GPU is much easier to support than on a PC because the OpenGL ES driver is running on the GPU itself. You just talk to it through a mailbox interface.

No, there are plenty of closed components with only binary blobs and header files for the programmer. But bare metal coding on it is still very doable and popular.