Terraced house and balcony extension

I have a question about an existing property, specifically a terraced house in Rhineland-Palatinate.

Is the resident of the middle house allowed to build a balcony up to the boundary of the outer house? This would mean full view of the other property from the resulting balcony. Apparently, a privacy screen is planned, but due to different terrain heights, depending on the viewing angle, it will be higher than 3m?

According to the state building code, I find distances of 2m to the boundary? However, it always talks about the opposite boundary, so I am not sure if there are no special regulations for terraced houses?

The question is not so easy to answer, especially without extensive information about the existing planning law (e.g. development plan) and the building situation (site plan, year of construction, heights, dimensions of the balcony ...).
If the balcony does not protrude more than 1.5m beyond the wall, it is disregarded for the distance areas. However, as you have correctly noted, this only applies to the wall from which it protrudes. The state building code remains silent on the lateral effects.
From a planning law perspective, terraced houses are considered closed development where boundary construction is prescribed. This does not necessarily require congruent boundary construction. However, if the balcony exceeds a building boundary, an enforceable defense option could be derived from the regulation, which actually does not protect neighbors.
Since building approval authorities are often uncertain in such cases themselves, they like to require neighbor approval in order to avoid litigation risk. If the authority grants the permit to your neighbor without your consent, the litigation risk naturally lies with you. If it is a very painful thorn in your side, only specialist legal advice can help.

Well, there's no development plan since the house(s) have been standing since 1915.

Ultimately, I don't really care about the balcony, but since it's a terraced house and consequently the windows are very close to each other, I don't want the summer barbecue smells coming from the directly adjacent balcony into my windows, not to mention the cigar-smoking neighbor, or lack of sunlight because suddenly a privacy screen might appear on the balcony. In an apartment building, the landlord can forbid or prohibit certain things.

Here I can't do that because there are two owners. Therefore, this means hoping for understanding, or disputes may arise.

Furthermore, the balcony, due to its proximity to the boundary, also represents a certain decrease in value or a deterrent effect for potential buyers should the property ever be put up for sale.

I don't feel like having summery grill stench that then drifts from the directly adjacent balcony into my windows, not to mention the neighbor who smokes cigars,

I call that: very factual arguments. He can do that from the terrace next door as well. I think a townhouse resident should be aware that he has neighbors in a townhouse from whom he notices something, so such arguments are smoke and mirrors for the authorities.

Here I can't do that because there are two owners.

??? My husband and I also had a townhouse, so the house had two owners... or did you mean that there is a separate residential unit upstairs? Is that even legal? Maybe you can make something out of that argument.

In the meantime, the building authority has confirmed in a conversation that the balcony basically requires a building permit. Due to the proximity to the boundary, windows, and light rights, our approval must be obtained. If not, and the thing were installed without permission, dismantling/demolition is threatened.