Wood privacy fence - planning over the top? Alternatives?

What exactly is the worse problem, Kati - the thumping in the living room or the noise on the terrace? If you had one wish...

Has the neighbor placed his speaker facing your house and if so, couldn't he change that?

But I don't know if I really have any legal grounds there. Maybe the music isn't "too loud"

There are limit values, measuring devices, and experts for that. For an objective measurement. Have you already done something in that direction?

Get advice from a soundproofing specialist, anything else is just guessing.

Sundays and public holidays are rest days; he is not allowed to play music then.

Sorry, that is nonsense.

Everyone has to refrain from noise then.

That is correct. Music is not always the same as noise. No one can be forbidden to listen to music as long as the manner is not suitable to regularly disturb someone. OP has already said that she is sensitive and possibly objectively the music is not even too loud. Try this: Next time the bass is booming, move either on the terrace or in your living room. Does the bass change its volume depending on the position? Are there positions where the bass is very low or very loud? If this is the case, there are standing waves and one can deal with them.

Music is not always the same as noise. No one can be forbidden to listen to music, as long as the manner is not suitable for regularly disturbing someone.

But that is obviously the case here.

Privacy screen to the neighbor after 1 year for under 150 euros. For approx. 8 m

No. The TE is clearly and self-certified not a regular case.
Another example: If I were bothered by someone resting on the city bench in a skirt that is too short, that would be my problem alone. Only if that person were naked there could the authorities intervene. The law is supposed to protect the freedoms of everyone, and if someone has special sensitivities, that is not always included.
Unfortunately, it’s not all that simple.
As a former disturbed-by-noise person, I had to gain my own experiences and was very thoroughly informed by the friendly people in blue. And that really was no longer just a sensitivity when schnitzels were being pounded at 2 a.m.
Quote: "You cannot forbid anyone from preparing food after the late shift." Fortunately, the neighbor was stupid enough to regularly listen to loud music, but even then I would not have gotten further without another neighbor who was also sensitively disturbed and incredibly persistent.

But the case here is apparently different. That’s why I would openly seek conversation here. Feel free to tell about your experience in the old apartment, that you have been somewhat sensitive since then. Whether they would be willing to test a bit with you. And above all, that they pay attention to turning off the music when they are not outside anyway.