I had overlooked that the extension is only single-story. However, the increase in dormers is also counted, since a building application is being submitted or it is a connected construction measure. Whether you stay under 50m², you have to check yourselves - and if you go over, just submit it first and see what happens.
Where is all the money going? The extension should be around €50,000. Then a new roof structure with roofing, another €70,000. And the rest for interior fittings?
The facade renovation, if it is not included yet, also adds €100-200/m². Either ETICS or ventilated with wood or brick. If you are doing everything anyway and need a new heating system, you should make sure to achieve a KfW efficiency house standard, then there are some subsidies, but the energy consultant will tell you about that.
If the result really looked similar, demolition wouldn’t be necessary, especially if what remains is still good without building sins/botch jobs. I am also more a fan of renovations (we ourselves revamped a lower 1959 bungalow last year - significantly below your renovation budget).