Maybe wallpaper works like this

arch-config/.config/sway/config

@@ -5,16 +5,19 @@
 # Read `man 5 sway` for a complete reference.
 
 ### Variables
-#
+
 # Logo key. Use Mod1 for Alt.
 set $mod Mod4
+
 # Home row direction keys, like vim
 set $left h
 set $down j
 set $up k
 set $right l
+
 # Your preferred terminal emulator
 set $term kitty
+
 # Your preferred application launcher
 # Note: pass the final command to swaymsg so that the resulting window can be opened
 # on the original workspace that the command was run on.
@@ -39,7 +42,7 @@ input * {
 ### Output configuration
 #
 # Default wallpaper (more resolutions are available in @datadir@/backgrounds/sway/)
-output * bg /home/exu/.cache/betterlockscreen/current/wall_dim.png fill
+output * bg ~/.cache/betterlockscreen/current/wall_dim.png fill
 #
 # Example configuration:
 #