I've been in a similar situation before, and I understand how frustrating it can be. The error code 0x00000709 typically relates to permission issues or conflicts when trying to set a default printer. You've already tried some solid steps, but sometimes a deeper dive is necessary.
Before modifying the registry, which can be risky if you're not familiar with it, I’d suggest creating a complete backup of your registry and your important files, just to be safe. If you decide to proceed with the registry changes, follow a detailed guide carefully. Typically, you would navigate to HKEY_CURRENT_USER\Software\Microsoft\Windows NT\CurrentVersion\Windows
in the registry editor and check for any entries under "Device" that don't align with your intended default printer.
That said, I've also seen success by uninstalling the printer completely and then reinstalling it using the latest drivers from the manufacturer's website. Sometimes these errors can be tied back to driver compatibility issues with Windows 11.
If you're still uncomfortable with the registry tweaks, it might be worth reaching out to Microsoft Support or checking out the Microsoft Community forums for more hands-on guidance. Also, have you tried setting it as default through the old Control Panel interface instead of the Settings app? Sometimes that can bypass glitches in the newer UI.
Were any of these steps something you've already tried, or do you need more detailed assistance on any of them?