Flooring for children's rooms: pros and cons

And what do you think about bamboo? Apparently, it is more durable than parquet, there are also good offers, and it looks good.

No matter what kind of floor it will be, I would always put a carpet over it in the playrooms. Consistent removal of shoes, no eating, drinks, and no water play.

That is an excellent theory. Children are not machines that follow rules, and constantly enforcing the rules ultimately costs far more than a dirty floor – you simply wear yourself out unnecessarily in everyday life. Children are impulsive, get excited, play, and often forget the surroundings. They should be allowed to be children. The floor covering should adapt to that, not the other way around. The OP is already taking the right approach to ask for a good solution.

Also tiles in the children's room are not an option at all, sorry...

That's what I always thought too. But at the end of the day, we ended up with tiles: unfortunately, it is the only way to be 100% sure that nothing off-gases, since they consist 100% of clay and purely mineral components. Tiles have been used for centuries and have proven themselves. All the new types of flooring, just wait and see what people find out in 30 years about the "completely harmless" chemicals in vinyl, laminate, and design floors. I mean: not that long ago, people also thought asbestos was a great thing and formaldehyde in residential insulation was completely harmless. So far – as of today – I simply lack any long-term experience.

Untreated wooden floorboards are still an option for me (rather not with underfloor heating and risk of splinters), but even current real wood parquet is glued in several layers onto carrier boards (with what glue?) and additionally sealed on the surface.

Therefore: tiles with a tactile wood structure and play rugs on top in sizes suitable for cleaning or even for regular replacement.

I am absolutely not eco-friendly and am aware that "sustainability" in building materials is more marketing than anything else. But make a list of all types of flooring and evaluate the floors regarding all criteria important to you such as price, suitability for underfloor heating, comfort in summer/winter, durability, indoor health, installation costs, appearance, and so on and so forth. Tiles somehow always win narrowly here, because apart from being "cold to the feet when the underfloor heating is off," they have no real weaknesses but many advantages and are comparatively inexpensive.

Tiles relatively cheap? Only if you lay them yourself. Otherwise probably the most expensive flooring besides parquet.

All these new types of flooring, just wait and see what will be discovered in 30 years about the "completely harmless" chemicals in vinyl, laminate, and design floors. I mean: not so long ago, people also thought asbestos was a great thing and formaldehyde in residential insulation was completely harmless. From today's perspective, I simply lack the long-term experience.

I see it similarly, though not quite as strictly. We agreed: we will not buy from a store that smells like "new flooring." The method is certainly not foolproof, and it is probably possible to buy pollutant-free goods in such stores—but it seemed to us the only tangible option.

Tiles relatively cheap? Only if you install them yourself. Otherwise probably the most expensive flooring besides parquet.

Exactly, we are already at that point, installation makes it significantly more expensive than parquet. Especially since our "dream parquet" is currently on sale and quite affordable at €40.
And we had the problem with tiles without underfloor heating in our old apartment: The children sit on ice-cold floors.