How will this affect Tivo cable card users?

that is not the info the channel lineup page.

  If your television is connected via equipment other than a mini box, such as a Cox HD receiver or a Cox-provided CableCARD together with a CableCARD compatible retail device (and a Cox-provided Digital Tuning Adaptor for certain channels), programming is available in high definition only at the HD Channel position - typically the four-digit number above 1000.

www.cox.com/.../channel-lineup.html

available in high definition only at the HD Channel position

This is a recent change so Cox probably hasn't updated their web page.

These "positions" are called Virtual Channel numbers and are sometimes remapped.  Virtual Channels are what you press on the remote control and not the actually frequency of a transmission.

The "big" networks insist lower Virtual assignments so their programming isn't buried deep within the program guide.  I remember when Fox first launched and there was lots of contention for lower channels.

I think providers screwed up back during our transition from analog to digital TV.  If Digital TV was to be the future, why didn't the providers originally map (assign) all HD channels to the 2- or 3-digit equivalent and make SD channels 4-digit.  "Oh...we didn't want to confuse everyone?"  It would have been better to confuse us then rather than now.

how recent the same language about the hd channels is on the channel lineup pdf printed September 2020

I understand.  These lineups...web page and PDF...are working references to provide the current channel assignments.  A lineup wouldn't be of much use if it listed future or proposed assignments.

I would assume the schedule printed or dated December 2020 would reflect the then-current lineup.

This is just a remap of Virtual Channels.

TV networks go by lots of names.  For example, the name of its national or local affiliation (NBCUniversal), the name of the station (NBC4), the callsign of a station (WRC-TV), UHF or VHF frequency of the station and its provider-assigned Virtual Channel (4).

Cox is responsible to assign the Virtual Channel (4) because they're amassing all these networks onto their cable boxes.  If you press "4" on a Cox remote, the Cox cable-box will tune WRC-TV.

The names of affiliations, stations, callsigns and frequencies are not changing...only the Cox-assigned Virtual Channels are changing.

Virtual Channels really depend of the local affiliates within different markets.  For example, when I lived in Maine, CBS was Virtual Channel 5.  Here's, it's 9.