Construction company does not respond after planning - What to do?

That would be too risky for me. I would have the contract legally reviewed and have a proper termination drawn up by the lawyer. Are you not going to build it at all now? Is the clause worded in such a way that it only concerns the property and you can get out free of charge? That is all too specific.

Why not just use WhatsApp?
After all, it’s about a six-figure contract amount, so I find this way of communication a bit too "casual"

Exactly - the introduction of the electronic lawyer’s mailbox shares the fate of Berlin Brandenburg Airport (BER).

An email fulfills the text form and is therefore no less valid than an ordinary letter. Neither provides reliable proof, even if the letter meets the formal writing requirements.
That you don't want to adopt this for yourself is probably due to your very personal inner BER - purely a matter of mindset.
More binding is DE-Mail. The system works, it’s just that somehow nobody seems to need it.

The beA serves a completely different purpose than you suggest here. Look it up. Its crash landing is, however, always a laugh in the industry.

I would go to a lawyer with the contract. Check whether the termination is valid and when, if applicable, the statute of limitations begins, i.e., when no further cost claims would be possible.

We even went to a lawyer some time ago. But he said we should try to resolve it this way first. In our email, we didn't write that we would cover all the costs, but that we would come to an agreement. Regarding the inserted clause, the lawyer said it could be good for us, or also bad because the construction company could simply say: "If you don't get the property, then you just have to try harder. Pay more!" Now I'm a bit uncertain again.... if the mentioned "statute of limitations" occurs, that would be perfect. On the other hand, I want to have clarity finally and put some pressure on them by asking. Our two termination emails were sent with read receipts. So they were read. Just not answered. Next call: - to the lawyer? - to the construction company? Or terminate again in writing?

so to a lawyer who says: it might be good or bad, I might not go again but to one with a clear statement... Legal advice would definitely be my next step.

But he said we should try to clarify it like that first.

What does this lawyer do professionally? That doesn't exactly qualify him to handle it so carelessly. One has to read a clause with such a condition very carefully, who is entitled or obligated to do what and when, and who has to notify whom by when and how about whether this case occurs. You don't just screw around with it with the attitude of "I'm not in the mood right now, just call him first, maybe he doesn't have one either." The opposing side could have a lawyer who doesn't see it so sloppily (and turns a template into a goal, i.e. puts a gun to your head five minutes before the statute of limitations expires).

What is wrong with the lawyer's statement?

The agreement in a personal conversation, at the end of which there is a termination/cancellation/whatever/..., is usually the best way. Of course, the lawyer earns more from a lengthy legal dispute, so hardly any lawyer will give this advice, but rather immediately shoot with cannons at sparrows and put the full program into motion. So that speaks more for the lawyer than against him.

That the clause is a double-edged sword, he is also right about that. And precisely because of this, an amicable agreement is the most desirable goal here. No emails, no threatening registered letters. Go there, seek the conversation on site, be honest and done. If it doesn’t help and it comes to a dispute, then what counts anyway is what is in the contract; that does not change now.

ps. If the agreement is not successful, I believe it comes down to the fact that the construction company pulls a broker out of their pocket: 5 alternative plots, one of which you have to take and build on, or you will be accused: you don’t actually want to build, which means the clause "subject to plot" would not be applicable, but rather termination with... 10% or whatever... penalty clause.