s/behaviour/behavior/
American English in our docs

I believe it would be somewhat helpful to expand 'anonymous' there as meaning 'not belonging to an object' as opposed to 'belonging to OBJ_ANON object'

I think this is misleading, because even VM_ALLOC_INTERRUPT allocations can fail. Might be it is better to say something along lines 'if a way to handle allocation failure at the caller is worse than consuming the last free page'. Then you could mention kernel page table page allocation as an example.

when allocating pages without a VM object ? It sound too strange to me.

This statement somewhat contradict the previous sentence. If you mean that VM_ALLOC_WAITOK can be only used with noobj allocators, then why state that it unlocks the object?

Perhaps mention that VM_ALLOC_WAITOK is invalid for obj != NULL there?
Otherwise it is still looking somewhat self-contradicting to me.

This text still leaves the same issue present. At least I find the text self-contradicting or confusing at best. You cannot unlock object when noobj allocator is used.

This is why I included "if any". I could perhaps expand it to, "if one is specified by the interface" but I am not sure how to make it less confusing.

You are saying that VM_ALLOC_WAITOK is only valid for _noobj functions, right? Why not to say it outright when the flag is listed instead at the end, after you said that !noobj + VM_ALLOC_WAITOK relock (which is not true because you should not pass VM_ALLOC_WAITOK at all).

More importantly, we set the md_page field that is read by a future call to a mapping function, e.g., pmap_enter, pmap_qenter, etc., when creating a PTE so that the PTE encodes the right memory attributes.

I find this confusing because vm_page_t is itself a pointer type.

To avoid confusion, this should explicitly describe the status of the lock upon return.