fix(system): enable uwsm and fix session detection to allow VM login

- Enable programs.uwsm for session management.
- Improve SDDM theme session detection logic to be case-insensitive and more robust.
- Perform a global cleanup of 'Nnomarchy' and 'org.nnomarchy' typos across all scripts and configurations.

bin/system/nomarchy-update

@@ -1,6 +1,6 @@
 #!/usr/bin/env bash
 
-# Nnomarchy Update Script
+# Nomarchy Update Script
 # 1. Updates the flake inputs in /etc/nixos
 # 2. Applies system-wide NixOS changes
 # 3. Applies user-level Home Manager changes
@@ -10,11 +10,11 @@ set -e
 REPO_DIR="/etc/nixos"
 
 if [ ! -d "$REPO_DIR" ]; then
-    echo "Error: $REPO_DIR not found. Are you running on a Nnomarchy system?"
+    echo "Error: $REPO_DIR not found. Are you running on a Nomarchy system?"
     exit 1
 fi
 
-echo "--- Starting Nnomarchy Update ---"
+echo "--- Starting Nomarchy Update ---"
 
 # 1. Update Flake Lock
 echo "Updating flake inputs..."
@@ -35,4 +35,4 @@ if [ -d "$REPO_DIR/.git" ]; then
     sudo git -C "$REPO_DIR" commit -m "chore: update system (flake.lock)" || echo "No lockfile changes to commit."
 fi
 
-echo "--- Nnomarchy Update Complete ---"
+echo "--- Nomarchy Update Complete ---"