Ex RE teacher here @Popcornn .
This is how I approached it. These are stories told by people trying to make sense of the world they lived in. They didn't have the science we have now, and their thinking was very magical - but people all over the world were doing the same thing, trying to make sense of what happened to them (like "why do bad things like Floods happen?") most of the time they thought some mysterious power must have caused it, and often because they must have done something wrong and were being punished by the powerful beings called gods. The people who wrote the bible believed that their god was the only real one and that other peoples gods were fake.
The stories they thought made more sense were written down and saved, along with other things like songs. Not all of the stories agree with each other, because they were written by different people at different times, so it's more like a library of books than one book.
I used to get one half of the class to read genesis ch1 and the other half to read ch2v4 onwards. Write down the order in which god created the universe and the things in it 😎 - two different stories, reverse order, right next to each other. Ch1 is a temple hymn, with a chorus.
In my experience children are perfectly capable of a critical analysis of religious texts, they can appreciate the world view and understanding of the people who wrote it without having to believe it, just as they can read the stories of the Greek myths.
Myths are stories written by people trying to makes sense of why things are happening to them. You don't have to set it up as a "true vs false" dichotomy, just get them interested in literature, stories and people. So much of our history, art, literature, relies on knowing these bible stories.
One problem you MIGHT have with a "children's bible" is that it's obviously heavily edited - if the editor / publisher is deeply religious then the editorial bias will show that in the way the stories are presented. Remember these are all translations anyway from Hebrew & Greek, and different English translations will have made their own decisions about some of the more difficult text.