Replace electric underfloor heating / alternative sought

We were also thinking about installing a new underfloor heating system. That would also require the bathrooms to be renovated

Why do the bathrooms then have to be renovated? What does "renovate" mean to you? Just replacing tiles and sanitary fixtures (not expensive, but cheap) or a complete overhaul and even a change of the floor plan?

We have calculated the total costs at around 100,000,

How did you calculate that?

Since the purchase price is not a bargain, no bank finances us including the renovation costs at that amount.

I’m going to turn that around now. So you have too little income to get a loan for the renovation. Correct? So €100,000 costs about €375 per month at 3% repayment.
On the other hand, you want to buy a house that produces heating costs of almost €450 per month.
How can you afford that then? Unrenovated, the house costs you the same monthly amount as renovated (if we calculate with new heating, underfloor heating, and even new bathrooms! with €75 heating costs per month).

Conclusion: You can’t afford either option.

Conclusion 2: Find a house suitable to your budget.

Thank you for your feedback :)
We are actually looking for an expert and an energy consultant with an on-site inspection.

@Badsanierung: if the old underfloor heating is replaced, the bathroom floor must be completely removed including screed and everything else (possibly also the insulation if it should be damaged). In the course of this, we would use new sanitary facilities, but would not change the floor plan (only in the main bathroom would we relocate/rearrange the shower and the bathtub. The walls would remain).

We can afford both option 1 and option 2, only the bank has a different opinion :-)

@Badsanierung: if the old underfloor heating is replaced, the floor in the bathroom must be completely demolished including screed and everything else (possibly also the insulation if it should be damaged). In the course of this, we would use new sanitary installations, but not change the floor plan (only in the main bathroom we would move/reshape the shower and the bathtub. The walls would remain).

Then the T€ 100 are calculated with a huge anxiety surcharge, with which after the move and the renovation you and the whole family can easily spend 3 weeks in the South Seas at a 5* resort and/or put the new Golf in front of the door ;)

Thank you for your feedback :) Actually, we are looking for an expert and an energy consultant for an on-site inspection. @Bathroom renovation: if the old underfloor heating is replaced, the floor in the bathroom must be completely removed including screed and everything else (possibly also the insulation if it should be damaged). In the course of this, we would use new sanitary facilities but not change the floor plan (only in the main bathroom would we move/modify the shower and the bathtub. The walls would remain). We can afford both option 1 and option 2, only the bank has a different opinion :)

I fear that this will not work so surgically. Usually, you make one hole and are shocked by what you see, which is why you open the next one, and so on. If you want underfloor heating everywhere, and it would only make sense to do it everywhere, that almost resembles a complete renovation. Wiring, doors, plaster, connections, etc....