Danish Furniture Oil was identified as
one of the culprits; a subtle but critical distinction. Primarily because it was used by one of the individuals first identifying the problem. Apple's HomePod support document only mentions oils as a possible cause of the rings... not Danish Furniture Oil - which is very specific.
Source. Relevant excerpt: "It is not unusual for any speaker with a vibration-damping silicone base to leave mild marks when placed on some wooden surfaces. The marks can be caused by oils diffusing between the silicone base and the table surface, and will often go away after several days..."
Googling "furniture oil" brings you a ton options, Danish Furniture Oil being but one.