I wouldn't. The likely outcome is that your email address is marked as spam.

Part of me thinks if someone couldn’t be bothered to make a single API call, no email is gonna change that. They probably just signed up while evaluating options and went with something else.

Yeah exactly this. Another possibility is that they are non-technical users who don't understand what your product is, and are actually looking for something else. I dunno what though or how you would find out. Do you see search queries that lead to your site?

As a user of the internet. I don't think I've ever done something in response to receiving an email from a product/service I don't use.

The only marketing emails I read are about products I already use daily.

EDIT:

If what you want is to give resources to get started, the moment to do that is when signing up.

"Thank you for registering with our services, here are some learning resources that will help you getting started: "

Just out of curiosity, what is such an API used for?

Is email marketing (aka Spam) ever not a bother?

If the answer isn't "yes" then it's not worth it.

I think you are asking for a wrong solution. Your problem isn't that users don't use your product, but you don't know why they don't use it.

I would consider doing an email questionare as It bearly doesn't count as spam on very slow day with nothing to do.