Is tree height on private properties regulated by ordinances?

In private law, this ultimately applies as well, only the cadastre and the obligation for gardeners to inspect are waived. Karsten

Yes.
And also in private law, the owner’s duty to ensure safety applies, so he may or must have his tree inspected to avoid possible liability for breach of this duty.

The final word in this matter belongs to the BGH:

"Shading" before the BGH
The Federal Court of Justice (BGH) dealt with such a case of neighbor protection. The south-facing property of the owners borders on a public green area. There stand two approximately 25-meter high trees (ashes). The owners demand the removal of the trees on the grounds that their garden is completely shaded.
BGH judgment of 10.07.2015, Case No.: V ZR 229/14: A property owner cannot require his neighbor to remove trees because of the shading caused by them.

Significant impairment of property

[*]For a defensive claim against the neighbor, here the municipality, for the removal of the trees, a significant impairment of the affected property must exist. Such impairment is absent, however, when it involves so-called negative effects such as loss of light, as here.

[*]The federal states have issued explicit regulations specifying the boundary distances to be maintained for trees, hedges, etc. In this case, the prescribed distance for fast-growing trees of four meters to the neighboring property was not only observed, but even exceeded.

[*]At most in severe exceptional cases can a claim for removal of the trees derived from the neighborly community relationship be considered. Jurisprudence assumes such a case when the neighboring property is shaded completely and year-round, thus excluded from any light incidence, which, however, was not the case here.

High requirements for the claim to remove shading trees on a property

The BGH thus confirmed the decisions of the lower courts (LG Bielefeld, judgment of 26.11.2013, Case No.: 1 O 307/12; OLG Hamm, judgment of 1.9.2014, Case No.: I-5 U 229/13). Essentially, it remains to be stated that high (building) law requirements exist for the removal of trees on neighboring properties and a claim is only granted in absolute exceptional cases. It depends on the state law provisions and the individual case. The municipality did not have to resort to chainsaws in this legal dispute.

(Source: Attorney Mattern)

In the hot summers, you will be grateful to have shade from the neighbor's trees.

However, in winter it is then completely dark because the sun is even lower. An air-to-water heat pump with photovoltaic would also have cooled in summer.

However, in winter it is then completely dark, as the sun is even lower.

Yes, as I said, you saw that before purchasing and gladly accepted it. Are the trees located to the south from your perspective?

Yes, unfortunately. As I said, it was actually unthinkable for most people to leave the trees standing as the client. Here you can see a bit better how close the tree is to the house.

That does not look like an old building to me, but rather the house is not even completely finished yet and was deliberately built so close to the tree, which was probably already there in full glory.