TLDR: No, it looks like Debian doesn't handle my bad graphics card any
better. Nothing for Trisquel 9 to learn from Debian here.
I tried an Xfce-flavoured Debian live ISO, and apparently my graphics card,
Debian and my monitor did not get along too well with each other. Screen
resolution fell far behind the monitor's native resolution. If you are
reading this on the Trisquel website (as opposed to the mailing list), see
the screenshot. I have not shrunk the screenshot, what you see is the
original resolution; it showed vertically stretched across my monitor's
height, but did not match that horizontally, resulting in the globe logo
losing its circular shape, for example. It was worse than any distro I've
tried, including the three versions of Trisquel that I've used.
As you suggested, I wanted to use lspci to test Debian's recognition of my
graphics card, but the Terminal did not know that command, apt knew no such
package, and neither did Synaptic; Synaptic did offer the usual plethora of
installable packages. When I came back to the computer after a break of a
couple of minutes, I think the screen was black and unresponsive, so I ended
my experiment there. I hope the absence of lspci is not because I chose a
wrong flavour of Debian. I had first tried the "standard" flavour which
confronted me with a command line; I did not know what to do, and tried Xfce
instead. I assume "standard" does not include a desktop environment.