First off, a clarification... you stated " I understand you are not seeing the body of the email messages after moving them to a created folder on your Mac". That is not correct. If I open the email I can see the body just fine. The problem is when I open that mailbox (the one on my Mac that contains all 'Sent' mail items), the list of emails in the mailbox show the 'From' address (which is me) as opposed to the 'To' address. If I open my regular iCloud Sent mail folder, all the emails show the 'To' address. But copying/moving those messages from the iCloud 'Sent' folder to a new mailbox On My Mac, now what I see is only the From address. Clearly if you have a folder/mailbox of sent emails, you want to be able to see who they are 'To', not who they are from - you know they are from you!
I did run a little test this morning... I took one of the 'Sent' emails from the folder on my Mac and copied it back to the iCloud Sent folder. When I opened the iCloud Sent folder and scrolled down to that message it now shows the To address, yet in the On My Mac folder it showed only the from address.
I expect you could test this very easily... in Mail, create a new mailbox on your Mac. Select some emails from your iCloud Sent mail folder and copy them to the newly created folder. Now open that folder... I expect you will see the same thing!
To answer your questions:
The email account is iCloud. I have other email accounts, but I forward all mail to my iCloud account. iCloud is the only one enabled in Mail.
My Mac is at all current software levels. Note that I have two Macs - a Mac Pro and a MacBook Pro... both are current on all software. This same issue occurs exactly the same on both.
I created a new user account, signed in with my iCloud iD. Signed in with the new account, opened mail, created the folder/mailbox on my Mac, copied some emails from Sent mail and it behaves exactly the way my normal accounts function on both my Macs.
I expect this has to do with the changes to the mail app in Catalina where now you cannot select which columns show when viewing a mailbox. But, obviously the normal iCloud Sent mailbox has some parameter set that tells it to show the To address (whereas the Inbox shows the From address)... seems like when you create a new mailbox it must just assume it contains incoming mail as opposed to outgoing mail?