For our purposes, the OpenGL renderer string from current
Mesa is about as good as it gets. When we have drivers,
the driver best knows how to handle whatever PCI etc.
devices it found, and it's also tied to the current X server,
which makes the most sense.
If you're wondering why GNOME is in fallback mode, the
lspci output isn't going to help a lot more for a bug report;
for that we need a lot of info from Xorg, kernel, etc. That
would be a separate script.