I’ve used this plugin forever (and since the new plugin developer took it over from it being abandoned about 5 years ago) - Post SMTP Mailer/Email Log – WordPress plugin | WordPress.org
Is this the one you’re using?
If so I recommend making sure your administrative user is the one on the Wordpress settings page - https://goodbudsme.com/wp-admin/options-general.php is the email you’d like to use. If you want to use a top level email from your domain I have better suggestions than relying on your host for assistance.
On your contact us page you are using a gmail. If that’s what you’d like to use and it is not in the WP setting then I understand the failure. I presume though that you are trying to use your domain mail and that is why the ports are failing even though your host guarantees the ports are open the way your MX is setup is the failure point.
The SMTP plugin relies on several factors and you are using “webmail” from your host which is a sore point in using SMTP anyway. If you hosted your mail on Google Workspace (small cost but if your in business should not be an issue to spend $10/month for reliability) or MS365 etc… Free Gmail is also and option and read below (I guarantee it will use the ports correctly as it has nothing to do on the server)
The reason why it shows success on sendgrid and mandrill is because you can offload mail using CNAMES with one of their free levels of service. If you want to use gmail then put your gmail (at least to test) in the WP settings page or get a workspace account either/or.
Workspace for professional mail is recommmended unless your a Microsoft person then I’d suggest MS365. Then you have 5 top level MX records (workspace) to do mail professionally and it will work out of the box. If you go with gmail or google workspace then you have the choice to build an actual app on google to deliver your mail from WordPress. (You will have to ensure the admin mail address is updated and the easiest workaround for this is to change it directly in your database on that USER ID line) if your mail is not working.
I host many woocommerce customers using these methods including the Sendgrid or Google APPs products and since they rely on us to make sure their customers are getting every mail, it would be a nightmare if we hadn’t used this setup going on for over 10 years.
You may be hesitant in moving your mail for fear of messing something up. Don’t be. I’ve movex folks from webmail to Google Apps, to MS365 and even Zoho (read below) and not everyone needs to migrate their mail but the mail on the previous server doesn’t get lost even when changing MX records. The records only serve to point and make the mail work.
Another free option (although I don’t recommend this as much as the ones above) is Zoho domain mail. It works reliably but doesn’t do the relaying of mail as good on a free account. A paid account on Zoho is (I think) only about $2 bucks a month.
I feel the frustration you must be having and DNS my sound easy from the outside but you have to work in it often to get comfortable.