Illegal construction without minimum distance to neighboring property

If the OP were to sell and the new owners objected, would the "illegal neighbor" still have to remove the approved constructions?

No. These would be legalized. A buyer buys as seen. If it bothers him, he doesn’t have to buy.

And would the OP or a successor still be allowed to build something within the mentioned 3m boundary distance?

Yes. A deviation would have been granted.

that the boundary violation doesn’t bother you?

There is no boundary violation. That would be an encroachment. A shed or a garage could stand there completely legally. To be able to assess how restrictive the building actually is, many details are missing here. Therefore, I would like to learn more about the situation on site (site plan, aerial photo, windows, heights, etc.) before joining the "chop his head off!" calls.

But who guarantees to me that with my signature no mischief is done and I then still end up with a land register entry?

The conversation with the building authority. I don’t know what you are supposed to sign and whether this path without the formal assumption of boundary areas would be supported by the building authority at all. A common procedure is that a more or less short text is written on the building documents, which is then signed, e.g.
I have taken note of the building project. I agree with the boundary distance shortened to 2.30 m, insofar as no building law consequences arise for my property from this.
Only what is stated in this declaration is acknowledged by you. No further consequences can be derived from this, certainly no land register entries.

Did this mean that she declared herself not harmed only under the aspect of neighbor protection (which made it easier for the district office to waive the demolition order)

Yes.

and a declaration to assume boundary areas could not yet be "forced" out of her

Yes.

but rather required further active cooperation (in the form of a notarized declaration)?

Yes. It is important that the form "Consent according to Art. 6 para. 2 BayBO for the assumption of boundary areas" or a declaration with the same wording is not signed. Therefore, definitely have the authority advise you when it is clear what is being sought from the neighbor.

The conversation with the building authority. I don’t know what you are supposed to sign and whether the path would be supported by the building authority at all without the formal adoption of the setback areas. A usual procedure is that a more or less short text is written on the building documents, which is then signed, e.g.
I have taken note of the construction project. I agree to the reduced boundary distance of 2.30m, insofar as no building law consequences arise for my property from this.
Only what is stated in this declaration is acknowledged by you. No further consequences can be derived from it, especially no entries in the land register.

I have already addressed exactly this issue with the seller, asking whether such letters could be issued by the district office, which was denied.

What really annoys me is that at the first meeting, the building permits were handed over almost without comment and it was hoped that they would be signed without problems.
When that did not happen, it was noticed that the child had fallen into the well and only then was the truth revealed.

Yes. A deviation would have been granted.

If a deviation has no consequences (e.g. dismantling, fines, or minimum distance), why are building permits applied for at all?
Then I (or anyone else) can just build something on the boundary and insist on a deviation and get away with it?!

I have already addressed this exact issue with the seller, asking if such letters could be issued by the district office, which was denied.

The letters are not issued by the district office, but the district office can explain the legal consequences. And if the employee is not completely stubborn, he should also offer help with phrasing. Well, it is not his task, but oh well, he shouldn’t make such a fuss, and if he does, you don’t sign anything and he has more work enforcing the then due regulatory measures.

If a deviation has no consequences (e.g. dismantling, fines, or minimum distance)

Sorry, I expressed myself incorrectly. The deviation is not granted, but an application for approval of a deviation is approved. If you do not sign, the authority will not dare to approve the application, since due to the undershooting of the minimum distance, publicly protected neighboring interests are affected. And thus the deviation does have consequences for the unpermitted builder.

Then I (or anyone else) can simply build something on the border and then insist on a deviation and get away with it?!

Only if the neighbor agrees and no further interests are affected.

My brother-in-law had exactly the same situation after buying his house. Neighbors coaxed him accordingly to design a new building that violates the boundary distances. Simply but firmly say, you don't know what you want to do with the property later and therefore the fairest solution is the one provided by the state building regulations without any recognition of boundary distances at your expense.....

Neighbors have coaxed him to design a new building that violates the boundary distances.

For what purpose?

The neighbors planned a new building directly on his boundary, for which he was supposed to give his consent..... And not just a small garage, but a two-story house right away.... and he was supposed to quickly sign because from now on it would cost money with the developer.... ouch!