Your existing integration already fits.
We answer on reCAPTCHA's and hCaptcha's own script paths and return their verify shapes, so the markup and the backend call you already have keep working.
How it works
The same globals and the same fields
A reCAPTCHA integration keeps its g-recaptcha-response field; an hCaptcha one keeps h-captcha-response. Your form and your request handler are untouched.
The same verify response
Our endpoints return {success, challenge_ts, hostname, error-codes}, so most libraries need no change beyond the URL.
Or use the native API
If you would rather not run through a shim, there is a first-party REST endpoint and server SDKs for Go, Node, PHP and Python.
What that means concretely
Each of these is a statement about how the product behaves, not a description of how we feel about it.
Drop-in migration in PrivCaptcha: common questions
What drop-in migration actually does, and where it stops.
Change two lines. Keep the rest.
10,000 verifications a month are free, and the integration is the one you already have.