This isn't dial-up Internet service. Why is everyone complaining that users should use broadband instead of dial-up?
Tivo came along before broadband was popular so the method of getting program data was to dial-up directly to Tivo to download that data. This was the only method on the first Tivos (series 1) which stopped being supported in 2016 when they changed the guide data. Your Tivo would dial a Tivo number in the middle of the night and download program data.
This announcement is mostly applicable to series 2 Tivos which could fetch program data over the Internet or by dial-up directly to Tivo. I'm sure they have so few of these things connecting that it will not affect many people. These Tivos are old. They can't even do 1080p and had analog tuners. The owners of these have been told you can still get program data you just have to do it over the Internet now.
I was notified even though my series2 has not fetched data for 10 years. It has a lifetime subscription so Tivo notified me just in case. Tivo is one company that actually supports really old hardware. They are not any Computer company that that tell your your computer is not supported after 3 years or a handset manufacturer who tells you that you can't get updates to android after two years.