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 {

site/layouts/partials/docs-navbar.html

 <header class="navbar navbar-expand-lg navbar-dark bd-navbar sticky-top">
   <nav class="container-xxl bd-gutter flex-wrap flex-lg-nowrap" aria-label="Main navigation">
     {{- if eq .Layout "docs" }}
+    <div class="bd-navbar-toggle">
       <button class="navbar-toggler p-2" type="button" data-bs-toggle="offcanvas" data-bs-target="#bdSidebar" aria-controls="bdSidebar" aria-label="Toggle docs navigation">
         {{ partial "icons/hamburger.svg" (dict "class" "bi" "width" "24" "height" "24") }}
         <span class="d-none fs-6 pe-1">Browse</span>
       </button>
+    </div>
     {{- else }}
-      <div class="d-lg-none" style="width: 2.25rem;"></div>
+      <div class="d-lg-none" style="width: 1.5rem;"></div>
     {{- end }}
 
     <a class="navbar-brand p-0 me-0 me-lg-2" href="/" aria-label="Bootstrap">
       {{ partial "icons/bootstrap-white-fill.svg" (dict "class" "d-block my-1" "width" "40" "height" "32") }}
     </a>
 
-    <button class="navbar-toggler d-flex d-lg-none order-3 p-2" type="button" data-bs-toggle="offcanvas" data-bs-target="#bdNavbar" aria-controls="bdNavbar" aria-label="Toggle navigation">
-      <svg class="bi" aria-hidden="true"><use xlink:href="#three-dots"></use></svg>
-    </button>
+    <div class="d-flex">
+      {{ if eq .Layout "docs" }}
+        <div class="bd-search" id="docsearch" data-bd-docs-version="{{ .Site.Params.docs_version }}"></div>
+      {{ end }}
+
+      <button class="navbar-toggler d-flex d-lg-none order-3 p-2" type="button" data-bs-toggle="offcanvas" data-bs-target="#bdNavbar" aria-controls="bdNavbar" aria-label="Toggle navigation">
+        <svg class="bi" aria-hidden="true"><use xlink:href="#three-dots"></use></svg>
+      </button>
+    </div>
 
     <div class="offcanvas-lg offcanvas-end flex-grow-1" tabindex="-1" id="bdNavbar" aria-labelledby="bdNavbarOffcanvasLabel" data-bs-scroll="true">
       <div class="offcanvas-header px-4 pb-0">
@@ -45,12 +53,6 @@
 
         <hr class="d-lg-none text-white-50">
 
-        {{ if eq .Layout "docs" }}
-        <div class="bd-search" id="docsearch" data-bd-docs-version="{{ .Site.Params.docs_version }}"></div>
-
-        <hr class="d-lg-none text-white-50">
-        {{ end }}
-
         <ul class="navbar-nav flex-row flex-wrap ms-md-auto">
           <li class="nav-item col-6 col-lg-auto">
             <a class="nav-link py-2 px-0 px-lg-2" href="{{ .Site.Params.github_org }}" target="_blank" rel="noopener">