feat(ui): add search clear button

Search now exposes a small icon-only clear button whenever a query is present.
Clicking it clears the term in one step and returns focus to the input so users
can immediately type a replacement.

The button uses the existing topbar styling language and a compact circled-x
icon alongside the keyboard hint.

Test Plan:
- git diff --check

Refs: user redesign nitpick about one-click search clearing

crates/lanspread-tauri-deno-ts/src/styles/launcher.css

@@ -223,6 +223,22 @@
 .search input::placeholder {
   color: var(--t-3);
 }
+.search-clear {
+  display: inline-grid;
+  place-items: center;
+  width: 22px;
+  height: 22px;
+  padding: 0;
+  border: 0;
+  border-radius: 999px;
+  background: transparent;
+  color: var(--t-3);
+  cursor: pointer;
+}
+.search-clear:hover {
+  color: var(--t-1);
+  background: rgba(255, 255, 255, 0.08);
+}
 .search-kbd {
   display: inline-grid;
   place-items: center;