2009 Nissan Murano’s radio mysteriously jumps stations

mysteriously changes radio stations without touching controls

Is your radio self-contained, or is it controlled by other switches external to the unit?

A failing body control module can cause weird stuff. https://moduleexperts.com/5-common-symptoms-failing-body-control-module-bcm/

Can you change stations from the steering wheel? If so, those buttons or your clock spring could be starting to fail.