I am not using a website unless you consider my cell phone service a website. It is a photo I took with this cell phone, which I select and no message. The server handling my incoming email is my website provider and I did contact them... my email provider. And, I am receiving all kinds of emails from many places because I am a professional artist and many contacts, galleries, organizations, other artists, etc. I mentioned above, this is my personal artist website. FASO is one of the largest artist website hosts. They immediately got back to me and couldn't find any issue from their side. No issues with their email service.
Remember this is my cell phone (iPhone) photos that I click on the little square with an upward arrow at the bottom, which let's you choose text, email, etc. I send them by choosing "mail" and input my email address and a subject. Then hit send. For years they have been going to my inbox in my website email with no problems.