Apple Mail Rules Applied to Gmail Keep Coming Back

I am at a loss and have seen several posts about the same or similar issue (copy and paste the subject line into Google to find them) but there are no solutions other than having different mail apps for different mail accounts. It appears it is a technical challenge that Apple is unable or unwilling to solve.

I'd like to use rules to manage emails I receive in Mail on my Mac to automatically organize the emails into folders on my Mac.

My understanding is that for Gmail it labels emails rather than using actual folders, perhaps similar to prefix labelling in object storage. As a result when a rule is applied to an email, it moves a copy of the email to the appropriate folder on my Mac but it seems the label is either not removed or the email is not deleted from the Gmail inbox by sending it to Gmail trash.

When Apple Mail checks for new mail it downloads the same message again, so during an email session I am re-applying rules to clean up the inbox dozens of time since the email I am reading is now hundreds of messages away from the next unread email. For example, right now I have 175 messages in my inbox, I select all of them and then select Apply Rules to have 169 emails moved to designated folders and I am left with 6 email messages. A few minutes later Apple Mail checks emails again and 169 email messages come back and I'm back to 175 messages.

If I manually move a message to the designated folder, then it seems to have been removed from Gmail because when it checks email again I now only get a total of 174 email messages. The point of having the rules is to save my time in manually moving 169 email messages to various folders by using rules to "manage incoming email messages and automate tasks, such as replying to or deleting messages."

Perhaps I can manually check emails instead of automatically checking, but I'd rather have new emails automatically downloaded.

So, in a nutshell I would like to have a rule applied to incoming emails that will copy the email to a designated folder and then inform Gmail to remove the email in the exact same way as if I manually dragged the email from my inbox to the designated folder defined in the rule.

a) Is that possible?

b) If it is possible, is Apple willing to implement it?

To me it seems simple; when the rule is applied call the same code that executes when the email is manually dragged to the folder. Perhaps it is not that simple?