When Diana died, BBC1 and BBC2 both took the same ident and announcement with a generic BBC logo* (I believe some on here have said it was called the 'family ident'). By the time of the Queen Mother's death though the policy had changed and both channels introduced the news with their own idents and announcer (with BBC Two infamously getting the timing wrong and having to wait several minutes on a static ident).
Sounds as though that is still the policy, but would the death be officially announced after 7pm when BBC Four is on? How long would they delay the news if it happened later at night?
*gratuitous plug: https://telly.site/diana/
Unless anything has changed in the last couple of years, the article is incorrect on that detail and the procedure for going into the initial news bulletin is not the same as it was in 2002.
Yes, it would still be announced after 7pm, I'm not sure what the cut-off point is before it would be left until 8am the next morning (8am has always sounded quite late to me but it is what has been reported in various places), probably something like 10 or 11pm. And, supposedly, it won't be announced until the next day if it happens on Christmas Day.