Does the municipality want to purchase shares of my land?!

Something is not right there.

I see it the same way.

Everything is in order, the notary checks whether there is a land charge or a right of first refusal registered in the land register. If the municipality (or someone else) is noted here, there is a period of four weeks to exercise the right of first refusal. If this does not happen, it is considered waived.

After signing the purchase contract, the notary should immediately inform the municipality about the purchase contract so that they can check whether a statutory right of first refusal exists and, if so, whether they want to exercise it. Either the notary slipped up or you expressly waived waiting for this declaration. Both are then at least questionable. In the first case, you would have to check whether the notary is liable for damages.

The sale was then processed as usual, which also involves notifying the municipality.

And precisely this notification comes right at the beginning, before the usual purchase processing. That way no additional costs arise because the municipality steps into the purchase contract and thus also pays all fees.

I see it the same way.

After signing the purchase contract, the notary should immediately inform the municipality about the purchase contract so that they can check whether a statutory right of first refusal exists and, if so, whether they want to exercise it. Either the notary dropped the ball or you explicitly waived waiting for this declaration. Both are then pP. In the first case, you would have to check whether the notary is liable for damages.

And this notification is right at the beginning, before the normal purchase process. This way, no additional costs arise because the municipality steps into the purchase contract and thus also pays all the fees.

Attention, there is a difference between "informing about the sale" and "sending a copy of the purchase contract."
The only ones who dropped the ball in my case are the officials from the municipality.
The municipality was informed in the course of signing the purchase contract; I have this in writing.

The legislator stipulates that the municipality has the right to request the purchase contract; as far as I know, no deadline is defined for this.
As soon as the purchase contract is sent by the notary to the municipality with the consent of the seller and buyer, the municipality has two months to intervene in the purchase contract, as I already wrote in my previous post, but only under certain circumstances.

The only ones who dropped the ball in my case are the gentlemen from the municipality.

I don’t see it that way. §28 Building Code:
(1) The seller must immediately inform the municipality of the content of the purchase contract.

I have that in writing.

So it has been done.
If a pre-emptive right does not exist or is not exercised, the municipality must immediately issue a certificate upon request of a party involved.
Was the request made? Did you receive a certificate? If you can answer both with "yes," the municipality dropped the ball and forfeited its pre-emptive right.
If you did not receive a certificate, it is your risk to proceed with any steps.

The legislator provides that the municipality has the right to request the purchase contract; to my knowledge, there is no defined deadline for this.

If the municipality has been informed about the existence of a purchase contract, it has two months to issue a decision.
(2) The pre-emptive right can only be exercised within two months after notification of the purchase contract by administrative act against the seller.

Was the application submitted? Did you receive a certificate? If you can answer both with "yes," the municipality slept on it and forfeited their right of first refusal.

That's a good point, thanks for that!
After the notary sent the notice of sale to the municipality on behalf of the seller, he should actually have waited for the delivery of the certificate before informing me of the release for payment.

Since I already received the notice from the notary in mid-August—two weeks after signing the contract—that he was giving me the "green light" to pay the first 50% of the purchase price, I of course transferred the amount immediately. Moreover, I have also paid all invoices that have come to me so far for notary fees, property transfer tax, registration fees, etc.
I never received a certificate from the municipality or the like.

As a layperson, I had no knowledge until now that I had to wait for a certificate from the municipality. I was under the impression that exactly because of such intricacies a notary is needed for the handling of real estate purchases.
Maybe that is exactly why the notary is currently keeping a low profile...
I will try to arrange a personal appointment with him in the next few days.

he should actually have waited for the delivery of the certificate

That's how it should be.

I never got to see a certificate from the municipality or the like.

Because there isn't one anyway. The municipality wants to exercise its right of first refusal.

I was under the impression that exactly because of such tricks, a notary is needed for the handling of real estate purchases.

Among other things. He is your contractor, you pay him, and he should act in your interest.

I will try to arrange a personal appointment with him in the next few days.

Then let's hope you won't need an appointment with a lawyer afterwards.
If the notary is actually at fault, he might be able to make up for it in the negotiations with the municipality that are still necessary now.

What annoys me primarily is that I have already invested a lot of money and working hours in renovating the upper floor.

How high are the investments in the house so far?