Div into <p> but outside of <p> after saving the content

I believe we need to register the element as a block level element rather than an inline element.

At https://ckeditor.com/docs/ckeditor5/latest/tutorials/widgets/implementin...
Take a look at this bit of the page: inheritAllFrom: '$blockObject'

We need to implement that here: https://git.drupalcode.org/project/ckeditor_div_manager/-/blob/3.0.x/js/...

So I think this:

schema.register('divContent', {
  inheritAllFrom: '$inlineObject',
  allowContentOf: '$root',
  allowAttributes: ['class', 'title', 'id', 'lang', 'style'],
});

Becomes something like this:

schema.register('divContent', {
  inheritAllFrom: '$blockObject',
  allowContentOf: '$root',
  allowAttributes: ['class', 'title', 'id', 'lang', 'style'],
});