By attaching a roof terrace to the conservatory structure, the conservatory loses its character and thereby becomes an extension.
This reasoning is as vague as the terms terrace, conservatory, and extension themselves. Unlike a full floor or the floor area ratio, the law does not define these terms, since a building part that only minimally deviates from the definition would legally no longer be classified in this category. Therefore, the building authority has discretionary power in this matter. If you removed the panes of the conservatory, you would no longer have a roof terrace but a balcony or, if the supports were also removed, a balcony. According to the development plan, these should not exceed the building boundary (I assume). However, from the neighbors' and urban planning perspective, your roof terrace would have the same effect. The approval procedure does not mean that your request is not approvable. It just does not fit the exemption from approval, since it must be examined whether the construction still fits into the urban design or not.
Would you recommend that we first obtain the written consent of both neighbors (left and right) for the building application and attach these letters to the application?
If the setback areas are observed, the rear building boundary should have no protective significance for the neighbors, and exceeding it would not violate the neighbors' rights, so their involvement is not necessary. However, if obtaining the signatures is unproblematic, it could be helpful.