Yes
I'm curious because you make it sound like you did that explicitly? When openssl would be pulled in as a dependency anyway.
I just installed sddm to have a look and on my fully updated system there are no library errors.
sddm links to libssl.so.3
❯ ldd /usr/bin/sddm | grep ssl
libssl.so.3 => /usr/lib/libssl.so.3 (0x00007fa41b160000)
world/sddm 0.19.0-9.1 is my sddm version
system/openssl 3.0.8-1 is my openssl version
You should be able to still access your system by booting and then switching to another TTY.
Hold CTRL-ALT-F2
There's various way to get your desktop back. Fixing your openssl issue is one of them. Make sure the system is fully up to date.
Run ldd /usr/bin/sddm and post the output.
You could just use startx for now https://wiki.archlinux.org/title/Xinit
Install xorg-xinit
sudo pacman -S xorg-xinit
Create ~/.xinitrc and add this to it
## Uncomment the three lines below if you use pipwire for sound
#/usr/bin/pipewire &
#/usr/bin/pipewire-pulse &
#/usr/bin/wireplumber &
startplasma-x11
Stop sddm
sudo rc-service sddm stop
Start X
startx
You could also switch to another Display manager eg. lightdm.