"Developer" inherits from "user". If it's good for users, it will probably be good for developers. True, users don't often read documentation. But if you have 100 users to each developer and even 1% of users read READMEs and, say, 50% of developers read them, you'll still have twice as many users looking at the README than developers. So cater for both.
Both non-developer users and developers will want to know two things to begin with:
- What does it do?
- How do I get started?
At that point, they're going to have more questions like
- How do I make it do the thing I want it to do?
- What does this thing do?
But the answers they are expecting may be very different (they may be hoping for answers to questions like "which button do I press?" vs "which source file do I need to edit?"). That's when you break it out into different documents. Point to the tutorials for everyone first, and then link to the developer documentation.