Neighbor wants to plant a mountain maple

That's completely fine, and you can design your garden however you want - even if your neighbor might have some objections to the bare simplicity...

Everyone interprets a garden differently,

Well, you can google the term garden - just look it up in the Duden or Wiki...
"enclosed land for the purpose of growing plants"

part of a garden may also be lawn

If you see it differently, you still have to respect the definition of a garden for your surroundings or neighbors.

On the other hand, you probably don't have to tolerate a sports field at the neighbor's

Just wait until you live in your house, the sunshade can't be split into four parts and keeps tipping over, the sun becomes unbearable, or you eventually find out that the best windbreak is a hedge

Yes, a lilac tree looks nice and won’t grow bigger than my house.

nice is relative - a maple is nice

You know what? Besides the taste issues, we overlook the real audacity. Namely that apparently you have to submit a planting plan at 305. Are you kidding me? My land, if I want to plant strawberries there, my land. If Christmas trees are supposed to grow there, my land. If there is supposed to be a lawn and a water play area, my land. And if I have a rabbit hutch there, also my land. What on earth does any authority have to do with that?! Which educators are at it again here? Karsten

Well, Karsten, there are many new development areas where entire forests are being cleared. Then the municipality supervises the planting of compensatory greenery. Or directly by the Elbe here, where the water stands, they try to retain the water with planting plans, i.e., root systems.
Neighbor law disciplines the growth heights of trees with clearance zones. I think that is fine.

For example, we are not allowed to plant thujas as a hedge. I think that is good because I don’t like cemetery plantings in rows.

Best regards in brief

On the other hand, I think the thing with the cemetery hedges is outrageous. Whether you like them or not is irrelevant; if I like them, I want to plant them. In return, you might do something I don't like, maybe even black, bare roof tiles. So what, everyone should be happy in their own way. Friedrich the Great. The man is right. Karsten

Everyone interprets a garden differently, for me it consists of...

Exactly, and your neighbor just has a different or even more taste.