The article/episode guide The Lockdown Season in DWM 554 unexpectedly contains a very useful quote from Peter Harness about his thoughts on the webcast:
I really enjoyed seeing how the two Osgoods have moved on. It’s always fun to check in on a favourite character. Ingrid’s a brilliant actor and lovely friend and she did a stellar job, as she invariably does.
I think it's clear that he considers this webcast to be part of the continuing story of the Osgoods in the DWU.
In addition, the description of the webcast by Steve O'Brien in the same article is as follows:
The first of the shorts set during the lockdown period, the two Osgoods Zoom-chat each other while in isolation, throwing up some fan-pleasing Easter eggs.
The Osgoods watching the in-universe Doctor Who is officially recognised as "a fan-pleasing easter egg" — no different from the TV series in Remembrance of the Daleks.