how to send business related emails from gmail while staying credible

Since you were considering using your existing work email and hide the logs from your employer I’m not sure my solutions would work. And I recommend you just don’t do that. If the email gets saved into some logs or forwarded to your boss by the other party it won’t end well (assuming you want to hide it for a reason).

If you have or want your own domain and not to pay for email, setup a forwarding service. If you use google domains it’s free to forward emails to your personal gmail and you can even make outgoing email look like they come from your custom domain email. Alternatively you can setup the same thing with mailgun.

Ps. Last time I used the mailgun setup I had the problem where if I made or accepted calendar invites my personal gmail would show instead of the custom domain.

By the way, if you're doing email marketing then be careful how you treat prospects in the EU. You'll need to segment them out. Here's how you can find out if someone works in the EU based just on their email address: https://www.inlistio.com/articles/find-out-if-someone-works-in-eu-gdpr-compliance

When you say "professional account" do you mean your work email address? I guess I'm confused about the use case and why you want to delete it from one account.