These are the steps I took to install (most of) GNOME 40 Debian Unstable:
$ sudo apt install -t experimental gnome-shell gjs mutter gnome-control-center gnome-desktop3-data
$ sudo apt-mark auto gjs mutter
Failing to install gjs 1.68 from experimental will result in white or blue desktop backgrounds regardless of the wallpaper you choose. This bug was reported in Arch.
Most of GNOME 40 functionality should now work, including the updated activities overview.
What doesn’t work? Settings->About still display GNOME’s version as 3.38. I suspect it’s because gnome-session is still at 3.38.
Update 2021-08-24: I upgraded to gnome-session 40.1.1 and it didn’t solve the version string issue.
Update 2021-08-31: Following a comment by Jeremy, I installed gnome-desktop3-data from experimental and it fixed the version string issue.
The version number comes from the gnome-desktop3 source package.
Thanks Jeremy. Installing gnome-desktop3-data from experimental fixed the version string in the About dialog.