I have a simple PowerApp based on a SharePoint Issue Tracker list. When a new item is added I want to send an Email to a group of people notifying the action. However, instead of coming from the user who created the new item, I want the email to look like it's coming from an Email distribution within the company.
First up, I created a flow in Power Automate, where an email is sent when a button is pressed in PowerApps. Pretty standard stuff, with only addition being "From (Send as)" set to the email distribution I want the email to look like its coming from. I have made sure that my account has "Send As" permissions to this distribution.

Next, from PowerApps, to the submit button, I added the following code:
SubmitForm(EditForm1);
EMail_Notification.Run(
varSendTo,
"New Item Added: " & EditForm1.LastSubmit.Title,
"EMAIL BODY HERE"
);
This works fine when I use my account to create an item, and I get the email as expected. However, when I try with a different user account, the flow fails with the following error message.
You are not authorized to send mail on behalf of the specified sending account.
It appears that even though I have the ownership of the flow, the user who clicks the button must also have "Send As" permission to the email distribution in order for this to work. I want all people in my organization to be able to use my app, but obviously I don't want to give everyone the "Send As" permissions to the email distribution.
Is there a way for a PowerApp to send email notifications appearing as coming from a certain email address?