Greetings, K1200R.
I see that you're having some problems exporting mailboxes from the Mail application on your MacBook on macOS Catalina. The problem is, another mailbox is created and it only contains a few emails. I'm glad to help with this.
Import or export mailboxes in Mail on Mac -- This article provides the information and steps that you need under "Export mailboxes".
How to use safe mode on your Mac -- If these were the steps you were using and the exported mailbox contains only part of the emails it contained, restart your Mac in safe mode and see if you can export the entire mailbox correctly now.
If the issue also happens while in safe mode, follow the steps under "If the issue continues in safe mode". If it doesn't, the steps to use is under "If the issue doesn't continue in safe mode"
Let me know how that goes.
Take care.