Inject equity or finance completely?

I completely agree with my predecessors in this case. Then you will be independent later. And in house construction, the land is also considered as equity.

As much equity as possible. However, you have to think it through if you end up without liquid equity afterwards... I wouldn't want to give up my "freedoms" completely.

I also agree with the previous speakers..... use all the equity available. The interest rates should not change much in the next 2 - 3 years and since you paid for the property with equity, you will get a great interest rate anyway

The question is how quickly you can build up liquidity again? If "only" three-digit amounts per month can be saved here, I would not put everything in. The 20-30k€ can also be financed variably at the local VR-Bank or Sparkasse without land registry entry.

This way you remain free in choosing the future financing and still have money in reserve.

You just have to consider that in addition to the house, the kitchen, furniture, lamps, small items, etc. are also included. Depending on the situation, that can quickly add up to several tens of thousands of euros. And the bank doesn't finance that for you like it used to with the mortgage.

Therefore, the question is what can be saved. If there is a large monthly surplus, then buy the property "cash" and build up as much equity as possible until the construction. I would not include the equity but keep it as a buffer and for the kitchen, etc., at least if possible. But that can only be seen then.