Thanks for remembering News 24 during that period.... I would ask when did the Breakfast branding took over the Saturday early slot?
I think this was discussed in the old thread and is a little off topic but to recap, Weekend 24 used to run 8-9am on BBC2 on Saturday mornings from shortly after the launch of News 24. This continued for many years but post-Breakfast launching in 2000, they'd just change to News 24 branding at 8 on a Saturday morning (W24 never appeared in the titles in that era!).
Following the September 11th attacks the weekend BBC1/2 slots weekend were extended. Previously N24 had been billed overnight till about 7am which meant that although Breakfast was there for the last hour, it wasn't billed. This changed in late 2001/early 2002. The Saturday slot however now became totally branded as Weekend 24 despite being virtually identical to the Sunday edition bar the titles. Over time they started bringing in some of the Breakfast format as seen in that clip. When the 2003 relaunch happened I do remember seeing "Weekend 24" text going round the globe once, but that didn't last long.
I'm not sure exactly when Saturday became Breakfast but it might have coincided with Saturday CBBC moving to BBC2 at the start of 2006 giving the programme a consistent slot, but might have been a little earlier.