Figured it out with the help of Adding 'Recent Items' to File Explorer & Open/Save Dialogs in Windows 10 - αlphαrithms. I'll condense that page here.
Open a Command Prompt as an administrator.
Enter the following command:
mklink /j "%USERPROFILE%\Recent Items"...
I'm running Windows 11 Pro 64-bit Version: 21H2 (OS Build 22000.527). I have added the Recent Items folder to Quick Access in File Explorer, and I would like to do the same thing in Save As and Open dialog boxes. I know this is possible because I did it in Windows 10 (but don't remember how)...