Remove redundant self-assignment watcher in navbar state

Co-Authored-By: Codex <codex@openai.com>

src/components/AppNavbar.vue

@@ -203,10 +203,6 @@ watch(
   { deep: true },
 );
 
-watch(filterName, (newVal) => {
-  filterName.value = newVal;
-});
-
 /**
  * Handles navigation when a navbar tab is clicked.
  * @param {Event} event - The click event from the nav item.