Good soundproofing elements near the property boundary - recommendations?

Because it is the truth. But you don't want to hear it. If the noise even bothers you inside the house, what should help outside?

I don't want to hear that because it's not true. Sound is waves, which can be absorbed or reflected. My question was not "if it works," but what is best suited for it. If you have no idea about that, better advise other people on things you know more about instead of claiming here "it doesn't work." "It doesn't work" does not exist.

So to contribute constructively. First, have all the glass in the windows replaced, we did that too. Of course, it’s bad for the environment and expensive to do afterwards, but there’s no helping it. It makes a big difference because normal triple-glazed windows are a disaster. You should basically only buy soundproof ones. Outside, I would build a 2m high wall to the neighbor made of larch wood, filled with suitable noise protection material. Alternatively, gabions.

I can imagine it to some extent and once it’s in your ear, it’s also hard to get out.....
My experience/idea on this:
Depending on the relationship with the neighbor, I would actually try to go through the neighbors, maybe everyone can do something good for each other. The moment just has to be right, maybe something will come out of a nice conversation by the fence.....that would at least reduce the cause. I think they might not even be aware of it. Maybe they feel similarly about something else concerning you.....who knows, and if you sit together once, you can just address it and ask if you can do something for them in return.
I don’t know your relationship with them but in my opinion that would be the most sensible, albeit perhaps the most unpleasant, way.

Since you even hear it in the house with closed shutters, sound reduction measures in the garden probably won’t help much. Therefore, I would first try a mobile or lightweight solution (boards with sound insulation in between, plants, or something similar) before having something expensive done that won’t bring you any benefit in the end.
We had a really tall and absolutely thick and dense-growing thuja hedge over the years; even though thujas were not the dream of my sleepless nights, they were really dense; before that I had the sauna/garden house standing there and it was a bit better; however, you will probably still hear such bass.

It’s not possible doesn’t exist.

I think psychoacoustics is great. Great idea.

google something like Gegenschallanlage (also gerne with option to build it yourself or also sometimes if interested Muzo). Something like NoiseCanceling headphones but in "large". There were also test versions for railway lines near residential areas. However, such a system is usually aimed at one point (where the person seeking quiet is located)

Otherwise, if the above-mentioned alternative is not an option, the wall to the neighbor should include sound-absorbing (breaking) elements. In the form of egg cartons or pyramid foam. With a bit more imagination and a lot of effort, you could also build that outdoor-capable yourself.

Please do not forget that LSW may possibly be a structure and require approval. Furthermore, under certain circumstances, static proofs may also be necessary. I live behind a noise barrier. Yet you can still hear every car if you are sensitive. But I do not focus on hearing the cars. Then you hear nothing anymore. You only hear the idiots who think that silencers are mandatory for fun. The same applies to your neighbor. Mutual consideration seems to be foreign.