This gets more interesting by the minute. So I did install my cable TV providers app on my Apple TV and it does in fact mimic what I get on the cable box. This then solves the issue because I can simply use the Apple TV to watch anything I used to watch via my cable box by using that app. This means the HomePod will do the trick! That's the good news.
The bad news is I just read that Apple has just discontinued the original larger HomePod and will now only concentrate on their newer smaller HomePod Mini :-(
I was interested in buying the larger HomePod for its sound and while I have not yet heard what the mini sounds like, I cannot fathom it will be as powerful to push out the rich bass that the larger one does. I've heard the larger one and liked it. I hesitate to buy SONOS for this but will now start looking at their products due to the discontinued notice on the larger HomePod.
So, while the issue I started here has been successfully NOT solved because you cannot connect a cable or TiVo box to the HomePod, at least I did find a way to address the situation by using the cable company's app on my Apple TV. I wonder if I can label my own post as a solution :-)