I have verified that as conjectured in previous posts, it is exactly the file
/System/Library/Desktop Pictures/Big Sur Graphic.heic
that controls the just-after-boot user selection screen in a multi-user setup (hereafter the "Login Screen" as many other posters have termed it). I have managed to modify this file and set the Login Screen to show my company's logo, as desired. I describe the procedure below, but first:
MAJOR WARNINGS: Following this procedure will apparently leave your Mac in a state in which you cannot use FileVault, and must leave both Signed System Volume (SSV) and System Integrity Protection (SIP) off. This almost surely violates the terms of any Apple Care or warranty you might have, and may leave your Mac more vulnerable to security breaches. This procedure appears to be very much a one-way street. Also, to perform this procedure you need to be comfortable using the command line in Terminal to manipulate files.
So, I cannot recommend that anyone follow in these footsteps. You have been warned.
In any case, here's what I did on my 15" MacBook Pro running Big Sur 11.4. The process is based on the information in the post at https://developer.apple.com/forums/thread/649832.
1) Boot into Recovery Mode (⌘-R while starting up). Open the Terminal under Utilities. Enter the two following commands that disable SIP and SSV respectively, and then reboot (normally).
csrutil disable
csrutil authenticated-root disable
2) Copy the C language code file at https://raw.githubusercontent.com/fxgst/writeable_root/main/writeable_root.c to a convenient place on your computer; I will just call this file writeable_root.c
3) Make sure that the `clang` compiler is installed on your Mac. This probably means installing XCode. (I am not certain because I had already installed XCode, and clang was present on my Mac, and I think that's why but I am not 100% certain.)
4) Open a terminal window, and change directories to the one where you saved writeable_root.c, and compile it with the following command:
clang writeable_root.c -o writeable_root
5) Now run the program with
./writeable_root
6) This command will place that Terminal in a special directory which can access the System files in a writable way. So make sure you don't leave that special directory - only change into directories inside it. In our case, we just want to go to the spot mentioned at the top of the post:
cd System/Library/Desktop\ Pictures
Note there is no initial slash in the directory name in this command -- we are not going to the usual /System/Library, but to the special view of that directory accessible from inside the terminal session that writeable_root has created.
7) You may want to save the original login image (the one that has been described as "vivid" among other things); for example, with:
mv Big\ Sur\ Graphic.heic Big_Sur_Graphic_original.heic
8) Now replace that file with whatever image you want to appear on the (multi-user) login screen. For example, to sub in the lovely nighttime photo of grasses along the Big Sur coast, just do:
cp Big\ Sur\ Night\ Grasses.heic Big\ Sur\ Graphic.heic
9) When the file is as you want it to be, just type `exit` to leave this special shell session. NOTE your Mac will now automatically reboot -- and show you whatever image you substituted in under this filename at login!
10) However, as mentioned in the warning, at least in my case, the Mac will no longer boot at all if either SSV or SIP is turned back on, and I am unaware of any way of undoing the above changes. Certainly re-running writeable_root and putting the original graphic back did not return my Mac to an "Apple-approved" state, in that it still would not boot with SIP or SSV on.
Hopefully this information is of interest to anyone out there with a sufficiently strong itch to change that login graphic that they are willing to forego FileVault, SIP, SSV, and Apple Care. Cheers.