Email was sending fine and now has stopped
When using mail() as your mail delivery method, CiviCRM will hand off to PHP's mail() builtin, which in turn usually hands over to a local delivery agent (see also PHP's mail configuration settings).

Unless the WordPress Gmail SMTP plugin does more sleight of hand than I anticipate, it won't get a say in how emails sent via mail() are delivered. WordPress mail plugins typically only get to intercept email routed through WordPress's wp_mail() wrapper. So based on your description (and my assumptions about WP Gmail SMTP), I think what happened is that previously your webserver was able to deliver via mail(), but now it can't.

You can investigate how it did work in the past by comparing the delivery headers of a previous WordPress generated mail (eg new user rego or password reset) with the delivery headers of a previous CiviCRM generated email. I think you'll find that they arrived via different routes.

Why they've stopped arriving is not so obvious. I'd try, in this order -


Check your PHP error log, which may contain more debug info about why mail() failed.
Check your PHP settings (via phpinfo()) to ensure that the mail configuration settings are correct/appropriate.
Check if the emails are being routed to junkmail; perhaps your mail host or the webserver config changed and the emails are being delivered but treated as spam. (Since CiviCRM says mail() failed, I don't think this is your problem.)
Check if the emails are being handled at all by your webserver, by investigating your webserver's mail logs. (How to do this depends on your server / hosting environment, you may need to request access from your hosting provider or contact a technician.)
Verify that your webserver is capable of delivering emails. (Perhaps some configuration changed, or the MTA daemon died and needs restarting.)
Verify your SPF / email configuration. (It looks OK from here, but you might find that your server is routing email over IPv6 and your SPF config doesn't handle this; that could lead to you being flagged as junk.)