Youre looking for a lockscreen. like people have suggested, id say the sweetest way is writing your own simple script. For example, take a look at my lockscreen script to get a feeling of things.

your can take a screenshot of the screen and blur it and set it as background each time.

https://codeberg.org/alirezaalavi/dotfiles/src/branch/main/sway-config/.config/scripts/swaylock-custom

u could use an custom bash file that screenshots ur desktops, blurs it, and then sources it as ur lockscreen from a config file, in bash it could go:

#!/usr/bin/env bash

bg=~/.lockscreen.png
grim -o $bg
convert $bg -blur 0x8 $bg 
hyprlock
rm $bg

havent tried it yet, but as long as ur sourcing the ~/.lockscreen.png on ur config file, or u launch ur locking program with an argument to use whatever u used as a background (and that way u can use mktmp instead of throwing it on ur home folder) it should work. Just try the commands b4 executing it since i wrote this from my bed on a saturday and my brain is half working.

i just used hyprlock as an example, since u said ur using hyprland, but u can use whatever ofc, I myself use swaylock.

what you are asking for doesn’t really make sense.

a display manager is for running when no user is logged in. its purpose is to log in and start your session. thats why they can’t show a desktop as a background because ot isn’t running yet. once you log in the display manager quits because its job is done.

You may screenshot the desktop after login and use it as a background, but I don’t think it will be exactly the same