This is hypothetical but had me wondering.

We shared a yard wall with a neighbour, double thickness with one brick
on our side and one on theirs butt up to the rear of our houses.

When they had a kitchen extension the yard wall went.
Their new kitchen wall is right up to the boundary but all on their side.
It was all amicable FWIW.

I was merely wondering (no plans) what would happen if we wanted to do
similar?

Would our builders build 2 skins of wall bang up against their wall?

Should there have been a small space left between their wall and the
boundary, then our builders would do the same and leave the silly sort
of gap I often see?
That serves no purpose other than to trap crisp packets!

Is it common to come to an arrangement with a neighbour where you use
their new wall as one of yours?
ie. their exterior wall as your interior.