I hope you are well today and thank you for your question.
You can achieve this as described on the below pages.
You can use the below plugins to add the contacts to the Mailchimp list submitted from Contact form 7.
Hi, I have tried to install “PublishPress plugin”, but it seems that cannot notify subscribers when a new post is published as the screenshot attached. Kindly advise that how to auto email to subscribers when a new post is published.