There's been some work in anesthetized rodents showing that glymphatic clearance is affected by position. Lateral (side) works better than prone (back) or supine (stomach). Of course there are two issues in relating that to sleeping humans. First, rodents - in spite of being the closest in the mamalian family tree to primates have a different 'scaling factor' of neuron size to brain size. And second, they were anesthetized not sleeping.
Without getting into the whole 'we don't understand how general anesthesia actually works' discussion - which is yet another rabbit hole I've fallen into. :-)
I'd also mention that I had a brain infection some years ago. I slept through most of my time in the hospital - and felt particularly driven to sleeping on my side to the point that I had a frozen shoulder* when I got to rehab. I'm normally a side sleeper, don't sleep well on my back so this bit of 'anecdata' probably means nothing - but that study certainly got me to wondering.
*all on one side. I normally switch sides through the night, but I had all these things attached to one arm that had just enough slack to be on one side only - so a frozen shoulder.