Though I'd prefer to have the BgInfo updated to handle newer video configurations, I have found that you can get around this by creating a Windows Shortcut to the BgInfo executable you use when editing your .bgi files.
Open the Shortcut Properties, go to the Compatibility tab, click the "Change high DPI settings, then check "Override high DPI scaling behavior", and select "System" (or System Enhanced). Click OK, OK to save the changes.
This change affects other parts of the BgInfo GUI, so I occasionally switch between my shortcut and directly on the .exe depending on viewing priorities.
This is launched from the .exe:
This is launched from the shortcut with modified DPI settings: