The left is a reset, the right is a reset and update.

The right is the better option, that's likely why the left is greyed out.

Personally I would use an ISO image directly from Microsoft and install a clean copy of Windows 11 that way. Dell drivers/software can be loaded afterwards from the Dell drivers page as needed.

In either case, none of the options allow me to format/partition the drive with the Dell utility, it seems.

When you activate Windows 11 by signing into your Microsoft account, Windows 11 will go out and download all the latest drivers in its database before you even get to the desktop.

My first image seems to keep failing. I blanked out the Service Tag as I did not know if how much it could identify anything here.

I had trouble using the dell software way a few times.  You can always download the ISO from Microsoft using the media create tool, and install from the ISO.  Then go to the drivers/downloads page for the R13, enter your service tag and download the needed drivers, alienware/dell software, etc.