Okay, so the previous teacher had not had any concerns, but the new teacher (of only a few months) does.
Friends of ours went through this in a primary school. After a new, unexpected negative assessment, they found out that the previous teacher had been gradually losing interest in teaching and had stopped making much effort, so that she just generally tended to write that all the children were doing fine, as she rolled down towards resigning. Then, when the new teacher arrived, she was freshly qualified and enthusiastic and had been told that this class had been somewhat neglected, so she went at everything with bright determination to pick up on all the deficits. Suddenly not just our friends' child but almost half the class had recommendations for therapies and extra support.
It took several interventions from parents acting together to get an experienced teacher come in to work with this class for a little while, to gradually assess where the previous teacher had been remiss and overlooked real issues, and where the new teacher was being over-enthusiastic.
Therefore: have you asked other parents about their experiences? You might also ask the teacher whether - since there's a difference between her assessment and that of the previous teacher - she has found this with many other children, in addition to your son.
In my experience, it works best if as a parent you meet the teaching staff with a ‚please can you help me‘ approach. The Swiss react badly to a direct ‚ I do not agree with you let’s discuss‘. Even if you want to confront them, don’t as they will run for the hills or dig their heels in.
I should add to this that the school thought there was something wrong with my daughter when she first joined kindergarten, recommending we talk to a psychologist. We declined knowing the behaviour they thought was odd was because she didn't speak the same language as the other kids, ending up playing by herself.
I have a kid in my class that I recently had a parent meeting with.There was a translator present and in this meeting the boy was a completely different child to what I see on a daily basis in the classroom. In the classroom this kid is totally blocked by his lack of language. To the point I have been thinking of having him assessed for autism! Then we had this meeting and he was able to speak in his home language with the translator. I literally could not believe the difference. He was actually animated and completely normal, I had never seen him like this!
So, it is very well possible that the teacher is seeing a completely different child in the classroom than you see at home and giving him that extra year might actually be very beneficial.
Also, your translation of the assessment is not right, "manchmal erkennbar" means "sometimes visible", not "unacceptable".
My daughter started kindergarten at 3 with no knowledge of Italian, had some problems at first, but now speaks it at home in Australia with her husband!