Time Machine & Apple mail icloud

I have had an issue with Time Machine back ups. if my apple mail app is open, then going into TM, the mail program is very small in size, there are no subjects showing for any of the emails, and even though there is a ladder on the right side I can go back in time. I’ve been dealing with this starting with. Catalina.

Tonight I bought a new MacBook air, set it up did a new TM back up, checked the back up a couple of hours later, checked mail same results unable to read any other than the most recent backup.

Called support, I was told because it apple iCloud mail TM does not back it up. Because all the emails are stored in my iCloud account no need to have it backed up twice.

Can anyone verify this to be correct?

Over the last 2 years I have spent countless hours on the phone, techs, senior techs, shared my screen, ran special programs, all nice all trying to be helpful, but no one ever told me TM does not back up apple iCloud mail

thanks

Seattle Mike