FWIW it’s super hard to benchmark since it just doesn’t have many features. There’s no syscall for memory management for a start. So if you have an application that uses this you need to create your own memory routines in that app.
At some point your app that successfully runs on this is doing all the things your os would normally do. At which point the os is superfluous anyway and the biggest optimizations are likely the highly tailored app specific routines you wrote rather than the specific os optimizations.
In the end a fair benchmark on this very minimal os would be an app that makes no syscalls since this doesn’t really support much anyway. If you run an application with no syscalls on a modern Linux with context switching tuned (you can fine tune how the context switching runs other threads) the impact of an os vs this is simply the memory overhead alone.
You just can’t compare this fairly. There’s no reasonable ‘how fast does this handle a malloc syscall vs Linux’ when it doesn’t implement a malloc syscall at all.
I think a fair benchmark would be some kind of task that this OS is particularly well suited for, and then implementing it relatively optimally on both platforms.
Hard realtime applications come to mind, though I'm not sure if BareMetal OS is suitable for those?