Is a letter of intent to purchase binding?

Of course, the letter of intent to purchase is binding. What else should it be? A reservation confirmation with risk for the seller if something on your side doesn't work out?

So I only know that in the [ungedrehten Fall] (when the seller suddenly no longer wants to sell) the potential buyer is out of luck.

According to case law, the declaration of intent to purchase is also generally subject to a notarization requirement, especially if a high contractual penalty is agreed upon. There are also exceptions, e.g., if one party signs the declaration without actually having a (purchase) willingness. There is a decision on this from the OLG Koblenz from 2017.

Is there also a "declaration of intent to sell" the other way around?

Of course the letter of intent to purchase is binding. What else should it be? A reservation confirmation with risk for the seller if something on your side doesn’t work out?

No, it is not. Just take a look at § 311b, Building Code: (1) A contract by which one party undertakes to transfer or acquire ownership of a property requires notarization. A contract concluded without observing this form becomes valid in its entirety only when the conveyance and the registration in the land register take place. If a prospective buyer breaches a duty of loyalty, for example by deceiving a seller and only pretending interest in a property (but why would anyone do that?), only then can a claim for damages arise. In practice, however, the burden of proof lies with the injured party, which will be difficult to provide unless the interested party clearly behaves improperly. Therefore, you cannot simply dismiss it so generally as you do and automatically derive a claim for damages from a letter of intent to purchase. You have to know the exact circumstances, which are likely to vary greatly from case to case.

Is this only about legal matters or about sincere and decent behavior? Whoever signs such a letter of intent to purchase and from the outset deliberately leaves the back door open not to buy if something becomes complicated or they find something better or... - should take down the mirrors at home.
If a society judges commitment to a promise only legally, it is going downhill.
Yes, that is very simple and very general – and not from a legal perspective, from which all sorts of arguments can be pulled out of a hat.