That is what is unfair about the Prior Approval scheme.
On the same row, some neighbours can be OK with 6m extensions, others aren't. At least with formal planning applications, it's the council which has the final say and it takes the personalities out of the equation.
A better solution would have been to go back to the 2008 re-cast of the permitted development rules and to have made the permitted 3m length 4m instead. A 3m extension is just too short for useful space when you consider the wall thickness; 4m would be more practical.
The proposal seems to breach the 45° line (if the policy applies) and there could an element of overbearing and enclosure leading to loss of amenity, so may not get formal planning permission if applied for.
May I ask how you got on? I feel for you as I am going through the same. Two planning applications after householder notifications blocked by neighbour. I am so stressed. We don’t have a lot of money and these neighbours are determined to make us pay if we have to now apply for full planning permission. It seems to me an envious neighbour has the final word.