I think I have read that after the creation of the development plan in 1996, newer state laws were introduced, which regulate, for example, boundary constructions.
There is planning law and building code law. Planning law is federal law, which authorizes municipalities to enact local statutes, and is mainly found in the Building Code (Baugesetzbuch) and the Land Use Ordinance (Baunutzungsverordnung). Building code law is state law and is mainly found in the State Building Code (Landesbauordnung) and the Building Submission Ordinance (Bauvorlagenverordnung, BauVorlVO). The development plan is a local statute and thus planning law. According to it, an auxiliary structure is a building structure that serves the intended use of the development area and is subordinate to the main structure. The garden house is a very typical auxiliary structure in the sense of §14 Baunutzungsverordnung, but also the pigeon loft, the rabbit hutch, the pool, a pavilion, a greenhouse... there is no exhaustive list since architects can be quite imaginative when naming buildings.
Justifications cannot be found in the development plan.
No, not in the development plan itself. But there must be a justification for every development plan explaining why it was established at all. And if the development plan generally excludes auxiliary structures, then the balancing process between § 903 of the Building Code
The owner of a thing may, as far as the law or the rights of third parties do not oppose it, deal with the thing at will and exclude others from any influence. and § 1 of the Building Code
(5) The land-use plans should ensure sustainable urban development, which reconciles social, economic, and environmental protection requirements in a responsibility toward future generations, and a socially equitable land use serving the public welfare while taking into account the housing needs of the population... must be reflected there. If it is not, this is a defect which at least justifies permitting a deviation under § 31 (2) 2. of the Building Code. Of course, the approval authority holds the upper hand when you need a permit. After all, who has that much time to wait for a court judgment if they want to build. However, in the case of your garden house, building code law applies. According to § 60 (Appendix 1.1), your project is exempt from the procedure. You do not need a permit. Yes, you still must comply with all regulations. However, if no justification for the general exclusion of auxiliary structures can be found, it is questionable whether the authority will proceed against your garden house. Is your planner familiar with local customs? Then ask him what he thinks about it. Otherwise, ask the planning office and the building authority and let one year pass without a negative response lacking verifiable justification.