reCAPTCHA v3 breaks user verification

Hi there. Your User Verification plugin seems to do exactly what I need it to do — separate real humans from spammers — but I can't get it to work on my site.

On a plain WordPress installation, without any other plugins installed, with a default theme, the plugin works as advertised.

But when I enable reCAPTCHA v3, using my site key and secret key, registration fails. The visitor fills in their username and an email, but when they click submit they get "Error: the username field is empty" and "Error: the password field is empty".

They are not redirected and no verification email arrives in their inbox. The account is not created.

The reCAPTCHA v3 icon is visible at the bottom right of the login page.