Your neighbors do not necessarily have to give their consent to a construction project. However, it does no harm, for example, when deviating from the development plan "such as by not complying with the setback distance of the roof terrace" to obtain the consent of your neighbors. The neighbor can approve the plan by signing, but he does not have to.
With your planned construction project, I would have submitted a building inquiry and asked whether it would be approved in the exemption procedure.
With us, the building authority had a reputation for often rejecting exemption requests (due to minor issues) so that the district office would also be involved. It does make a difference whether it costs 700 or 100 euros. :p