Non-compliance with the development plan by the neighbor

That sounds like a matter of interpretation. You can simply inquire with the responsible building authority. If applicable, the matter should also be reported there.

The terrace is annoying, but I don't see a removal here without a fierce dispute. I would probably approach the matter very openly. Take the neighbor aside and clearly say that the terrace is uncomfortably close for me. Therefore, there needs to be a privacy screen now and discuss how to come to an agreement. Everything nice and peaceful, and ideally immediately suggest a solution that you can ideally implement together. My favorite would be a hedge.

If the terrace is not permitted, the building authority may automatically take action for "illegal construction."

Then it is clear who tattled. Adults should be able to resolve their conflicts themselves instead of involving an authority. This option can still be taken later.

If the terrace is not permitted, the building authority may automatically take action for "illegal construction."

the authority probably has better things to do

The office usually also follows up on anonymous tips. I have already experienced that with much smaller matters with builders. For example, a basement door, because the new one was 10 cm higher and a new lintel was installed. The neighbor was bothered by the chiseling work. But he was not at home, he was at work. He would have liked to have been asked... Whoever is bothered should always be clear.