Yes. You are asking about verification of Recaptcha.
You have never actually checked to verify the user completed the captcha! That's your responsibility, it's not possible from the captcha to prevent form submission if it isn't completed.
How would recaptcha prevent
your form from being submitted until
you actually verify the user submitted a recaptcha response? In the same way, you could fail the captcha by selecting incorrect answers, and I imagine your form would still process.
YOU need to implement the error message saying "Please fill out the captcha". Once again, I included a link to the developer documentation describing how to do it.
I don't have any other information to share. You need to validate the user input in the captcha against Google as is described here
https://developers.google.com/recaptcha/docs/verify