I don't mean to clog up this thread with an unnecessary post, but I
just wanted to note that I (unfortunately) have had to use (as recently
as 2023-05-28):
debian-live-11.7.0-amd64-gnome+nonfree.iso
a number of times recently, due to flatpak being a corpulent space hog,
obnoxiously trying very hard to fill up my /var partition (10Gb, as
originally set by the Debian installer). But that is just a side
issue.
(Note: this is the Gnome Live image that has the non-free extra
drivers, etc., not the "standard" Debian Live image. Perhaps the
standard Debian Live image works differently; I never use it. And
note, this is Debian 11.7 (Bullseye), Debian 12 (Bookworm) may also act
differently.
I can state that in my experience, unequivocally, it boots into a Gnome
DE without any password needed. If administrative permission is needed
to do something, "sudo <command>" works, without having to enter any
password. Example:
sudo apt install timeshift
<ENTER>
This post is just a FWIW. Feel free to disregard.