Hello hypocrite
I suspect that the lady was responsible at the time for overseeing the renovation of the building envelope, possibly for a KfW program... without moving her ass to the construction site... which is a disgrace... and therefore the landlord should possibly hold her liable. Because if that were the case, she would have confirmed with her signature that the measure had been carried out correctly... which it was not!
The interior windowsill looks more like an artificial marble sill (pressed marble dust)... it also has no impact on the problem... tiles would have been just as fine... The interior windowsill always only contacts the frame of the old windows... for which there is a corresponding recess... groove. Moreover, it is always placed higher than the exterior sill.
However, as is and was common with massive or natural stone exterior sills, it may have been mounted too far under the window frame... if it is too long, it may hit the back possibly under the interior sill... fully or just barely... in any case not insulated. If you’re unlucky, there is nothing but an air gap or lumps of mortar there... In addition, during installation the exterior sills rest only on 1-2 lumps of mortar... normal mortar, that is... otherwise there is air all around... so no insulation.
If later only the front side was "plastered" there, then behind it there is now a significant thermal bridge..! Exactly what is showing here with you.
Ultimately, only the removal and renovation of the surroundings remains... and if you’re at it anyway... I wouldn’t hesitate to install a contemporary window right away... it’s not that big and expensive!
From a technical standpoint, the question also arises as to where the facade was "blown out"? This probably refers to cellulose insulation... inside or outside? Was the exterior windowsill renewed in the process? Or has it already been like that for 15 years (though it would still look good for that)?