When I send an email using the GMail API, I get an Access Token for the user to whom the message is to be sent and then when sending the message, I put some value in the Fro
No. The Gmail API is for Gmail users and service accounts are just for doing auth to a real Gmail account, they don't have their own Gmail account, etc.
If you want to send the email from some service, you need some bulk-sending email service like at: https://cloud.google.com/compute/docs/tutorials/sending-mail/ or something you run yourself or from some other provider.