Finance buying land or rather leave it?

As I said, currently one cannot say where the variable interest rate will move, therefore I still recommend taking out a fixed interest rate to avoid additional costs in case of interest rate increases.

That optimizes at the wrong end. The crucial thing is at what interest rate the house can be financed, and you have no influence on that today. If you repay the land quickly, it is relatively irrelevant whether the interest rate is 4% or 4.5%. No matter how many extra perks you negotiate so that the bank has a variable loan without a variable interest rate, that also costs money. If you have a fixed interest rate, you lose the flexibility to start earlier. Or later as well.

A build or purchase in the next 5 years is not planned, as we definitely want to move into an apartment in her hometown beforehand (provided that everything works out with home office) to have the family nearby.

Is there already building permission for the plot? So is there a development plan for it?

It is currently being developed and is to be sold afterward.