The contact form on my website says message successfully sent but the message never arrives in my email. Sendmail quota shows usage but no message being delivered to me. I attached some screenshots. Any ideas?

The contact form on my website says message successfully sent but the message never arrives in my email. Sendmail quota shows usage but no message being delivered to me. I attached some screenshots. Any ideas?
Localhost surely isn’t the SMTP?
Or is it?
We don’t provide SMTP
Google for SMTP GOOGLEMAIL
Then what sort of email service do you provide as my account says that I can send 50 emails per day?
I need to know what settings to use as I don’t want to use any 3rd party service just to receive an email from a Wordpress contact form.
Phpmail ()mail but it can be unreliable
Use Google SMTP