feat: Android download page, analysis retry and a collapsible search

- /android is a public page with the latest APK, the server address to copy
  and three install steps; linked from the sign-in screen and the profile menu
- failed audio analysis can be retried from the library page, which also shows
  the most common error; the analyzer no longer burns attempts on files that
  are missing because the disk is not mounted
- the top bar search folds into a round button and slides open on click, "/"
  or Ctrl+K

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

services/api/internal/auth/auth_test.go

@@ -565,5 +565,6 @@ func TestPublicRoutes(t *testing.T) {
 	e := newEnv(t)
 	assert.Equal(t, http.StatusOK, e.do(http.MethodGet, "/api/v1/server-info", nil).Code)
 	assert.Equal(t, http.StatusOK, e.do(http.MethodGet, "/healthz", nil).Code)
+	assert.NotEqual(t, http.StatusUnauthorized, e.do(http.MethodGet, "/api/v1/app/android/latest", nil).Code, "APK page is public")
 	assert.Equal(t, http.StatusUnauthorized, e.do(http.MethodGet, "/api/v1/unknown", nil).Code)
 }