You’ll want to look in your mail logs to identify what is happening with the attempted message sending.
Your goal is to identify where the mail process stops. It could be that PHP is unable to make the connection to the mail service. (For example, perhaps postfix/sendmail is not installed or running?) It could also be that your mail service is unable (or refuses to) route the mail on PHP’s behalf. (For example, your local postfix server or remote smtp server might not be configured to allow connections.) It could also be that your mail service does send along the message, but it is deemed unroutable or spamtrapped upstream. (For example, your sending might be missing compliance with policies like SPF and DMARC.)
When using your localhost as the mail server, first check your webserver error logs for any messages, then look at your local mailserver’s log (perhaps /var/log/maillog, or similar).
If using SMTP, first check your webserver error logs for any messages, then look in your SMTP server’s mail log (or ask your SMTP administrator for details on any error messages).
Either you will find a message describing the problem in your webserver error log or in the mail server’s message log; or, you will find a success message in your mail server’s message log, which means you need to look for policy compliance to avoid spamtrapping.