Move DocSearch out of offcanvas to always show it on mobile (#36824)

site/assets/scss/_navbar.scss

@@ -4,6 +4,12 @@
   background-image: linear-gradient(to bottom, rgba(var(--bd-violet-rgb), 1), rgba(var(--bd-violet-rgb), .95));
   box-shadow: 0 .5rem 1rem rgba(0, 0, 0, .15), inset 0 -1px 0 rgba(0, 0, 0, .15);
 
+  .bd-navbar-toggle {
+    @include media-breakpoint-down(lg) {
+      width: 4.25rem;
+    }
+  }
+
   .navbar-toggler {
     padding: 0;
     margin-right: -.5rem;

site/assets/scss/_search.scss

@@ -2,7 +2,6 @@
 
 .bd-search {
   position: relative;
-  width: 100%;
 
   @include media-breakpoint-up(lg) {
     position: absolute;
@@ -57,6 +56,26 @@
       opacity: 1;
     }
   }
+
+  @include media-breakpoint-down(lg) {
+    &,
+    &:hover,
+    &:focus {
+      background: transparent;
+      border: 0;
+      box-shadow: none;
+    }
+    &:focus {
+      box-shadow: var(--docsearch-searchbox-shadow);
+    }
+  }
+}
+
+.DocSearch-Button-Keys,
+.DocSearch-Button-Placeholder {
+  @include media-breakpoint-down(lg) {
+    display: none;
+  }
 }
 
 .DocSearch-Button-Keys {