What will the building authority say?

I see it differently, because in §14, "facilities" are mentioned regarding the points listed in §§ 2-13. Ancillary facilities are then introduced in § 14, and only those mentioned there, in my opinion, are excluded in §19.

I see it differently: By definition (see § 14 para. 1 sentence 1 Baunutzungsverordnung), parking spaces and garages/covered parking spaces (§ 12 Baunutzungsverordnung) do not belong to ancillary facilities. Ancillary facilities can, under the mentioned conditions, for example be: facilities and installations for small animal husbandry, garden arbors, tool sheds, greenhouses, composting facilities, locations for waste containers, saunas, playgrounds, swimming pools, combined heat and power plants, mobile phone stations, bus stops, among others.

Exactly, they do not belong to the ancillary facilities. But, in my opinion, in the old § 19 only ancillary facilities additionally mentioned in §2-13 are excluded from the calculation of the floor area ratio, so parking spaces and garages are not.

Building Use Ordinance 1977
§14, para. 1, sentence 1 states
Except for the facilities mentioned in §§ 2 to 13, subordinate ancillary facilities and installations are also permitted, which serve the purpose of use of the properties located in the building area or the building area itself and do not contradict its character.

and
§ 19 states
The floor areas of ancillary facilities within the meaning of § 14 are not included in the permissible floor area. The same applies to balconies, loggias, terraces as well as to structural facilities, insofar as they are permissible or can be permitted according to state law in the building line or in the spacing areas.

So terraces are not per se excluded from the calculation of the floor area ratio.

Exactly, they do not belong to the ancillary facilities. But, in my opinion, in the old § 19 only ancillary facilities additionally named in §§ 2-13 are excluded from the calculation of the floor area ratio, so parking spaces and garages are not.

Building Use Ordinance 1977
§14, paragraph 1, sentence 1 states
Apart from the facilities named in §§ 2 to 13, subordinate ancillary facilities and installations are also permitted, which serve the intended use of the plots located in the building area or of the building area itself and do not contradict its nature.

and
§ 19 states
The floor areas of ancillary facilities within the meaning of § 14 are not included in the permissible floor area. The same applies to balconies, loggias, terraces as well as to structural installations, insofar as they are permitted or can be permitted under state law within the building line or in the setback areas.

Therefore, terraces are not per se excluded from the calculation of the floor area ratio.

See! Where is the problem?
Floor area ratio (I) = The main building!-
Floor area ratio (II) = Main building + terrace + bicycle shed (equipment) + driveway (if not "water-permeable") ++!
for dog house + > 1m² must also be included respectively in the floor area ratio (II)

Well, that the floor area ratio (II) is probably exceeded .. see

Well, that the floor area ratio (II) is probably exceeded .. see

Correct. that is what the floor area ratio II indicates but here the floor area ratio II doesn't play a role

The development plan is no longer accessible now, but I only remember one street line that was not built on to the west

It seems that the Hells Angels then had a fling with the head of the building authority and were just able to prevent the construction of their "open-air commercial area"