We took the time to remove screws, re-position covers, adjust screw tightness, etc. No effect; doorbell speaker still buzzing.
So then we experimented with how the "indoor" person spoke into the app. There we found some success by having the indoor person hold the phone at arms' length, rather than near their face, or even on desk ("speakerphone" mode.)
The indoor person had to talk more loudly and "CLEAR-LY," but the clarity was better, as heard through the doorbell speaker.
My conclusion is that in the hopes of remedying previously-reported "low volume at doorbell speaker" issues, Ring may have offered a software update that OVER-amplified the voice transmission... leading to the "buzzing" that we are experiencing.
Other information, suggestions or opinions most welcome...