The thing that _did_ make a difference was changing a setting you can only get to via the Google Home app, so here are the details.
- Open the "Google Home" app.
- Select "devices" from the main menu.
- Select "settings" from the popup menu for the "silent" Chromecast device.
- Flip on the switch in the "Display" section labeled "Use 50Hz HDMI Mode"
BTW, the TV to which the Chromecast is connected is a little older but not so old that the default settings on Chromecast should prevent something as basic as _sound_!!! Thanks a lot Google!!
Anyway, with all the useless forum post chatter out there suggesting "turning it off and on again", "The IT Crowd" style, I thought it might be useful to post an answer that actually did work.