No indication website emails through contacts were ever sent

When I am on-line and have an opportunity to send an email through their website contacts, I can see my Gmail address as sender. But afterwards, there is no email in my sent email on iPhone or iMac.

it is as if it went into the abyss and was a waste of time and effort.

anyone else? I wish they would eliminate the person’s email address@icloud.com. Messes up things for eternity.