This is why branding is so difficult to define. It's always what it's not...this reminds me so much of the social media classes I took in college. No one can seem to define brand in a way that's easy to understand.
Branding is what people say about your product/service when you're not in the room is another way I've heard it described.
This is not really helpful when a person is trying to create a brand or add to a brand.
So, I'm just going to say...come up with what you want people to think about when they read your books. How do you want them to feel? Scared? Intrigued? Seduced? Happy? Reassured? Always entertained? This is what branding eventually accomplishes, but how do we get there?
If it was easy, I think someone would say, Branding is X. It's easy to describe X, so here's how you do it. Still haven't found any of those examples. If someone has one, please add it to the conversation.

For me, branding is overall for the business, then changes focus slightly for each genre, then gets more specific for each series and book. If you know what you want people to associate with your business, that's a great start. How do we get there?
Either we have an idea right when we start, or we try to constantly work on the brand as we go. If we start with a brand (and never change it) that can narrow our focus to the point where there isn't much room for anything new or outside of our original brand. This works very well for some people...I would get bored.
For me, I need to have room to be more creative, so I try to stay on brand in a general sense, but I'm always tweaking it to include new things. And that's why it's not "JUST" about the books. The books change, my ideas change, what I want to say years from now will not be the same thing I'm saying today.
If something is just too far away from my brand, THEN I consider putting it under another author name or even another umbrella/business. So far, that last bit hasn't happened, but if I decided to suddenly change to erotic romance, my brand would be over. That would have to go under an entirely new name, business, website, etc. because those stories would not be what people expect to find when they see my books, products, etc.
So, that's why branding isn't easy to define. I will leave you with one of my favorite examples of branding and actually my inspiration (even though I don't write children's books) because it's just such a cool site. Of course, I use lavender instead of turquoise, but this website is wonderful. Carry on and best of luck with branding!
https://peterrabbit.com/