> There are also plenty of 32 bit x86 machines still around
All x86_64 machines can also run 32 bit x86 code just fine. They have to - even modern CPUs start up in emulated 16 bit mode like it’s the 80s. They then they need to transition to 32 bit mode. And from there they can swap to 64 bit mode to run modern operating systems.
But you don’t have to do that last step. So this kernel should be able to run on any modern x86 computer on raw hardware just fine.