form is not sending email, but says 'successful'

The green Success message and not receiving any error messages is a very clear indication that CF7 is sending the email.

So your email is probably being seen as spam somewhere in the email process. This is usually due to email headers (in particular the From email address used) or email content.

Emails can be considered spam for a whole host of reasons and get rejected at many points in the email process in addition to your spam folder.

See Contact Form 7 Email Issues – this links to a much more comprehensive article which also covers emails being considered spam.

See also Best Practice to Set Up Mail.

If you find you need more detailed advice, after reading and working through the above links, please include a link to your Contact Form 7 form plus all your input in the Form and Mail sections of the CF7 interface. This should allow others to understand your actual problem and offer a possible solution.

I’m having the same issue on all four (4) of my WordPress sites that use Contact Form 7. I’ve tested each form, checked the spelling and CF7 settings, checked my spam folders, etc. Nothing works.

See https://www.codingmonkey.ca/my-contact-form-emails-are-not-being-sent-to-yahoo-hotmail-gmail/
See https://www.ads-software.com/tags/email-not-received