The most important question would be, (1.) whether the neighbors must be involved in the permission for deviation according to §66 ThüBO para. 1 in accordance with the “public-law protected neighborly interests” mentioned therein – which, for example, must also be taken into account according to § 31 Baugesetzbuch para. 2 – i.e. whether the signature is required.
In the crosspost, a construction expert has already given you the helpful hint regarding the judgment of the BVerwG 4 C 7.17 from August 9, 2018. While the judgment itself may still give you hope for defensive rights, the key points already indicate what the reasoning of the judgment clarifies: In order for the degree of structural use to have a neighbor-protective effect, very special conditions must be present. I do not see these in your case. And therefore, the obligation to involve the neighbors according to §69 Thüringer-Bauordnung is also not applicable.
You would have to prove the neighbor-protective character of the floor area ratio specification, which you will not succeed in, since on the one hand a different development plan applies to you and on the other hand, the impairments you mentioned are only indirectly related to the planning law floor area ratio. You directly complain about increased shadow casting, which, however, is regulated by the building code distance regulations. Only if errors were made in the calculation here or a related deviation was approved are your rights violated.
And (2.) does §17 Baunutzungsverordnung – with its upper limit of 0.4 in general residential buildings – apply in the development plan area?
The upper limit applies to determining the degree of structural use, i.e., for the plan drafters. However, they complied with the upper limit since they set it at 0.3. To check whether a concrete construction project is approvable, §19 Baunutzungsverordnung is applied, which allows several possibilities for exceedance:
... further exceedances of minor extent may be permitted ...
... As long as the development plan does not stipulate otherwise, in individual cases compliance with the limits resulting from sentence 2 can be waived ...
And this brings us to the many open questions of your two threads:
How do you know what your neighbor intends to build if you were not involved?
How do you know that he has received an exemption?
Where does the information come from that a decision was made not according to §31 Baugesetzbuch but according to §66 Thüringer-Bauordnung?
The described factual situation appears extremely confusing and imprecise. A deviation from the stipulations of the development plan, such as exceeding the floor area ratio, requires an exemption according to §31 Baugesetzbuch. Therefore, presumably no exceedance actually exists but only the utilization of the permissible exceedance under §19 (4) Baunutzungsverordnung. Furthermore, the Thüringer-Bauordnung does not even provide the possibility to build without approval according to §61 if stipulations are not to be complied with, so your information regarding the content of the preliminary approval of deviations (if it exists at all) is incorrect.
First try to obtain reliable information about the exact planning (site plan, elevations, exemptions, deviations) and the planning status (building consultation, building inquiry, building notification, building application, building permit) and formulate as precisely as possible in which rights you see yourself violated.