We spoke with two different chimney builders. It was about two things. First, the cladding of the back wall of the fireplace and primarily about stability. The fireplace does have a so-called cantilever, but it cannot hold the weight of the upper fireplace structure 100%. The cantilever is attached to the back of the fireplace in the base plate and pulls it downwards. The now additionally required and also commissioned 10 cm thick wall (as wide and high as the fireplace) will be connected to the room wall. Additionally, the fireplace will be anchored in the new wall. This is an empirical value from the last installations of the fireplace. A size smaller cantilever would have sufficed, but due to the structure of our fireplace, the additional reinforcement is necessary. If the cantilever had been sufficient, we could have alternatively taken a 4 cm thick fireproof Promat cladding. Ultimately, still acceptable in terms of price but a pity that this was only noticed so late. I just wanted to at least provide the answer since you all are always helpful with tips and advice.
Regards
Paule