See this article Use Smart Mailboxes to organize emails in Mail on Mac - Apple Support
If you change a message in a Smart Mailbox—such as marking the message as read or unread, or moving or deleting the message—the change is reflected in the mailbox where the message is stored.
An example screen shot .
If in your case , it is not happening either you have incorrectly set some settings in mail preferences or possibilities are mail application is corrupted and why the mail application gets corrupted you can use https://etrecheck.com/
and read by yourself the report what stuff is installed , also if there are slight irregularities in mail app its always better to delete from system preferences > internet accounts ( select the account and click on minus sign ) , it will get deleted from Mac .The mails are stored on servers so they will get downloaded .
Then you can again configure the mail app see this article Set up Mail on your Mac with email accounts - Apple Support