Is safety glass necessary or not?

Where is one supposed to fall from the groundfloor if one falls through the window?

You don't have to tell me. But that's just how it is...

That is the question: Do I have to comply with the DIN standard or not?

General answer: Yes
BUT: The DIN does not say that you have to install safety glass everywhere and at all times. It depends on the planner’s assessment and the traffic routes. For example, if a couch is in front of your window, it is clearly not necessary to choose shatterproof glass. The same applies if you go from the kitchen to the living room past the terrace door (and/or if the dining table is located there).

P.S. This has been stated in the state building codes/MBO in a similar way for almost 20 years. It is not new with the DIN.

For large-format panes, I would choose shatterproof glass. At my parents' house, one of the sliding doors shattered 10 years after installation, and the large shards slid downwards. Only by a miracle was no one injured. At the neighbor's, a large bird of prey flew into the child's room window, and the pane cracked some time later but did not fall out.

Where should one fall from the ground floor if one falls through the glass?

I'm not concerned about falling on the ground floor, but rather that our children crash their Bobbycars into the floor-to-ceiling windows and then something happens.

General answer: Yes

It now looks as if I have to comply with the DIN. But it says here that this does not apply to the private sector.

It now looks like I have to comply with the DIN.

I had written it somewhat like that too - the DIN does not necessarily require shatterproof glass everywhere. This is also confirmed by your link (please delete it immediately, otherwise you will receive a warning or worse). As I said, I don't do it either, and my window maker hasn't even come up with this strange idea.

It's not about the crash on the ground floor for me, but rather that our children ride the Bobbycar into the floor-to-ceiling windows and then something happens.

If it's important to you, why are we discussing this here?
Again, in the end, it will be a liability issue in your Bobbycar case. If the window manufacturer installs according to DIN and you don’t, then you have to release him from liability.

I can certainly find you a few articles where the opposite is stated.