So from my own "experience," even if I only perceive this as a listener. There are properties that simply cannot necessarily be calculated according to the cost approach. The colleagues just had a case where the calculated cost approach value was €240,000, but this was too low for all the involved appraisers. This was simply because the location is very sought after and there is definitely potential in the house. Therefore, in the end, a cost factor of 1.55% was applied to bring the house into the range where it is seen according to the appraisers' assessment.
It may simply be that in your cost approach this was not done. That means the pure cost approach must first have been carried out, right? Is there then afterwards a market adjustment, for example in the form of an applied cost factor (although this might not fit if there are hardly any comparable sales)?
There are also some pitfalls in the procedures for appraisals that can lead to the values not seeming to match each other. What does the financing bank say? That then also allows conclusions to be drawn, otherwise only the own market feeling (which is of course difficult when nothing or little comparable has been sold).