The way I see this rule is as follows - looking at both the video’s.
a C label / UK cert label is a label of conformity - the standard set for that class mark for the drone.
The drone is only of that class mark if no modification is added to it as that will change the spec of the drone. So if the label of conformity says that the drone is a sub 250g and it ticks all the boxes as per the manufactures spec then your fine - good to go - but if you change that spec from an out of the box drone that class mark is gone - its no longer valid so your C1 or C0 drone is no longer its a legacy drone pre class marks basically.
DJI has outlined what the payload limits are and what is OK in order that should you put a memory card in or an ND filter on it that it retains the class mark as its still within spec - but if you add drop system or a little Lego man on top of it then your out of spec out of class - this would also apply to the Air 3s too so basically you would have to follow the old rules of the over 250g for a Mini type drone and need an A2 CofC if you were flying in a built up area to comply.
Yes its crazy but people thinking that the still are in the class that the drone was spec’d at when they take it out of the box and add stuff on is a bit crazy as its no longer in spec to what was agreed with the CAA