“2023” is not actually hazy: if the BBC intended to broadcast what Tennant and Tate are filming now at Christmas 2022, they would have had to say that year when announcing it. It’s at least possible that when Davies says November 2023 he means for the series, not the specials, though I don’t think it’s likely. “Special” is short for “special episode,” after all, and I really doubt he’d written multiple full episodes for the new Doctor months before Gatwa was cast, or that they plan to do all the past Doctor(s) stuff ahead of the actual anniversary.
I have never known the bbc to ever state ‘we are filming this for x year’ not least because no one really pays attention when they are filming unless it’s something like who.
Aside from which… it’s Bad Wolf now, not the Beeb in-house (or even Studios)
I mostly remember the BBC tending towards saying things like ‘later in the year’ or ‘early next year’ whenever they talk about dates for *anything* unless pressed.
So what I am saying is… I don’t think it is a Christmas special for this year, but at the same time, I wouldn’t be entirely surprised if it turned out to be one, for a bunch of logical reasons.