Should I publish book chapters as standalone articles before approaching a publisher?
Publishers are going to look at your background before agreeing to a publish your work. Things looked at include:


Your citation metrics
Reviewers for your publication proposal
Your CV


Publishing some standalone articles will certainly improve all three, but you'd have less material when it actually comes time to publish a book (because the same material typically cannot be reused). So the question effectively becomes, "can I publish now or do I need a better profile?". Only you can answer that question, unfortunately.

If you don't know the answer either I'd suggest contacting a publisher now, and if they reject your proposals, then publish standalone articles first.