Continuation of construction despite the construction stop

In case of dispute, this is decided by a court.

The last two statements sound contradictory to me. Does this mean that a once approved building application cannot be contested by dissatisfied neighbors?

Let's assume that I want to build a bay window that extends 1m beyond the building window. This was submitted as such, somehow paid for and approved, the building application was granted. Can then any Susi Schneckenschiss or Hans Jedermann from the neighborhood still take action against my bay window? Yes or no?

If necessary, she issues a construction stop if something is illegal. Only then!

I think that is the problem. The issued building permit is no guarantee that the construction is actually lawful. Example: Federal Court of Justice ruling from 10.2.2011, Az.: VII ZR 8/10.

Okay, so no legal certainty through the building permit. Who has to bear the delay costs that may arise from the construction halt? The client?

The last two statements sound contradictory to me. Does that now mean that a once approved building application cannot be contested by dissatisfied neighbors?

Let's assume that I want to build a bay window that extends 1m beyond the building boundary. That was submitted, somehow paid for, and approved, the building application was granted. Can then some Susi Schneckenschiss or Hans Jedermann from the neighborhood still take action against my bay window? Yes or no?

To my knowledge, it works like this: the building authority checks everything before granting the approval.
If a point is debatable because there is an exception or an exceeding or something similar in the building application, then either the authority itself decides on it or seeks the opinion of those affected, e.g. the neighborhood, through their goodwill.
It can also happen that you are tasked with knocking on neighbors’ doors to get their consent.
Nothing is approved that could be subsequently complained about.

Citizen Authority: Case 1) I am the affected person: application-rejection-objection-possibly remedy- if not: lawsuit administrative court. I am not directly affected, but have an interest because indirectly affected: e.g. authority permits guesthouse in residential area, rental is excluded in the development plan, then: lawsuit against this approval. Consequence: possibly the judge orders an immediate stop of the guesthouse construction to protect rights or to prevent facts. Or: the building proceeds, I am right, then it must be examined afterwards how to deal with the guesthouse that was then created. (Possibly conversion into rental apartments?) In any case: an authority cannot order without question. The judiciary has the final word in case of doubt.