Get rid of high monthly annuity from an old mortgage loan

just be aware that the tax advantage is gone? In my opinion, you can't then offset the interest on the loan of the new house against the rent

Properly declare it in the new contract (or even two separate contracts - 1. for the rented condominium 2. for the new build). Then there is no problem with the tax. It could even be positive if a larger portion is taken out for the condominium ;-)