chore: drop vestigial $lib alias

$lib pointed at src/lib/, which does not exist, and nothing imported it.
Removed the dead alias from all five declaration sites (tsconfig plus the
vite and three vitest configs). A stray $lib import now fails fast as an
unknown alias instead of resolving to a missing path.

tsconfig.json

@@ -24,7 +24,6 @@
 
     /* Path Aliases */
     "paths": {
-      "$lib/*": ["./src/lib/*"],
       "$app/*": ["./src/app/*"],
       "$widgets/*": ["./src/widgets/*"],
       "$shared/*": ["./src/shared/*"],