fix search modal closing on keypress and add admin header icon

Track search_open as server state so morphdom doesn't reset display
to none on re-render. Move admin bar from layout banner to a gear
icon in the header actions. Extract layout_assigns/1 helper so page
templates use a spread instead of listing every attr explicitly.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

assets/js/app.js

@@ -380,6 +380,7 @@ const SearchModal = {
 
   open() {
     this.el.style.display = "flex"
+    this.pushEvent("open_search", {})
     const input = this.el.querySelector("#search-input")
     if (input) {
       input.focus()