Feasibility single-family house + land 550k-600k NRW

Since you seem to be so sure, I really had to ask the main income tax department head at the tax office again here.
It is definitely not correct or "allowed" in the private sector.
But it's basically already stated directly in § 9 para. 1 sentence 1 of the Income Tax Act.
The interest paid on debt does not serve the acquisition, securing, and preservation of income, as the rented property only serves as collateral and the loan agreement will also state that the rented property is merely pledged and that the financing is for another property.
I'm not saying it doesn't work, but it is not legal. So far, it only goes through very often because many offices are completely overloaded.
This exclusively refers to privately rented properties.

Thank you , as a layman I lack the right words there

The incurred interest expenses are not for the acquisition, securing, and maintenance of income, since the rented property only serves as collateral and the loan agreement will also state that the rented property is merely pledged and that the financing serves another property.

And why should that be stated? Of course, if that is expressly written, it doesn't work...
I financed a property. The financing serves the "(acquisition), securing, and maintenance of income" through this property.
With my existing equity, I can - as already stated above - do whatever I want. If there were an obligation to "use up" your equity first before obtaining a mortgage on an investment property, probably even more "showy cars" would be driving around and there would hardly be any private owners of investment properties.

As an example regarding the OP, the financing on the rental terraced house serves to "secure and maintain the income" because the existing equity is needed for something else - in this case a home of one's own and not a "showy car."

But just ask the head of the main income tax department - but please with the right story.
The question is, am I allowed to take out financing on a rented property and deduct it for tax purposes even though I have sufficient equity?

It doesn't matter at all. The money you get from the bank is used to build a private home for yourself and not to renovate/restore the rented property. You can twist and turn it as you like, it is not allowed. It just often doesn't come to light because no one checks. If you're so sure, then clarify the matter at the next submission of your [EST] declaration and see what happens.

The question is, am I allowed to take out financing on a property that is rented out and deduct it for tax purposes, even though I have sufficient equity

No, that is not the question at all. The question is: If I mortgage a rental property to buy my own house, am I then allowed to deduct the interest? Replace house with car, watch, vacation, etc. That clearly shows why it doesn’t work that way.

It doesn’t matter at all. The money you get from the bank is used to build a private home for yourself and not to renovate/modernize the rented property. You can twist and turn it however you want, it is not allowed. It just often doesn’t come to light because no one checks.
If you are so sure, then clarify the matter at the next submission of your income tax return and see what happens

The financing bank must secure the loan here in such a way that it is clear that a third-party property is being financed, otherwise the bank would be guilty of possible assistance in tax evasion. Because that is what it is!