You might get better response by starting a new "Discussion", (Start a Discussion) button on Verizon Messages Home screen. I am just a lowly Member, not a Community Manager, so I can't move your posts to another thread.
This Discussion thread has been building around the failure of Verizon Messages to "sync across multiple devices (smartphone, tablet, computer, and even smart watches) so you can keep the conversation going when you're switching between devices." as is claimed in the Microsoft Store.
But, your post did pique my curiosity, wondering if the failure you describe might be related to our sync failures.
I used my collection of devices and multiple email addresses and 2 cell phone numbers to check if I could replicate your problem.
I regret I won't be much help, as my tests worked as expected, no failure.
I composed a short text on my iPad Air in Gmail and addressed it to both my cell numbers (To:[email address removed per the Verizon Terms of Service], Cc:[email address removed per the Verizon Terms of Service]) as well as my primary email address (Bcc:???@att.net) and clicked send. (see appended screen capture)
The message was successfully received on both Cell phones/numbers (devices: Samsung Galaxy S9+ and BlackBerry Z30) and my @att.net email account, although it did provide me another example of our "sync across multiple devices" failure.
I have a vague long ago memory of Verizon saying that the #@vzwpix.com option was being eliminated. You might try another test case from Gmail to [full 10 digit number]@vtext.com, in case it was just a temporary server glitch.
Wishing you luck in solving your dilemma.