Which party wall notice for a garage conversion- can anyone help?

[Mortigua]

Has anyone done a garage conversion or does anyone know anything about party wall agreements for them please? Our garage joins to next door’s so we need to do an agreement but having looked at government templates I can’t work out which template is even the right one! Does it matter ?
Neighbour has seen the plans and is ok with it all. There are options online like “new wall astride the boundary “ notice? Or do we need “excavation and construction”?
Totally confused and trying to do as much as we can ourselves to keep costs low.

My next door neighbour converted their garage (part of the house, adjoining my staircase) into a habitable room & didn't need a party wall agreement, or indeed planning permission, as they weren't touching the foundations or digging. This was in 2015.

Thank you both. That’s really helpful to know . We do need one as the foundations are affected for drainage but I think we may have it now - Ben I may be touch if not though thank you and especially for the info on the new wall- they are reinforcing it but not building a new one so that narrows it down .