Create a 'search field' component for themes (#11045)

``searchfield.html`` is similar to the existing ``searchbox.html``, but does not
have the heading "Quick Search". Instead, it uses "Search" as a placeholder
text. This gives a cleaner and less cluttered appearance.

The searchfield component is added to the basic theme and thus can be used
in any derivative theme. It is not used by default for backward compatibility.

The searchfield compenent is made the default in the sphinx13 theme.

CSS changes ensure that the top of the search field is aligned with the
top of the main content.

doc/_themes/sphinx13/layout.html

@@ -32,7 +32,7 @@ <h3>{{ _('Navigation') }}</h3>
 {%- block content %}
 <div class="document">
   <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
-    {%- include "searchbox.html" %}
+    {%- include "searchfield.html" %}
     <div class="sphinxsidebar-navigation__contents">
       <h3>{{ _('On this page') }}</h3>
       {{ toc }}

doc/_themes/sphinx13/static/sphinx13.css

@@ -68,6 +68,7 @@ div.sphinxsidebar {
     overflow-wrap: break-word;
     margin: 0;
     padding-right: 15px;
+    padding-top: 0.5em;
     font-size: 1em;
 }
 
@@ -127,6 +128,10 @@ div.sphinxsidebar li.current > a {
     display: none;
 }
 
+div.sphinxsidebar #searchbox {
+    margin: 12px 0 20px 0;
+}
+
 div.footer {
     background-color: var(--colour-sphinx-blue);
     color: #ccc;

sphinx/themes/basic/searchfield.html

@@ -0,0 +1,23 @@
+{#
+    basic/searchfield.html
+    ~~~~~~~~~~~~~~~~~~~~~~
+
+    Sphinx sidebar template: search field.
+    This component is similar to searchbox.html but does not include an
+    extra heading ("Quick search"). Instead, it uses a placeholder text
+    in the search field.
+
+    :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+    :license: BSD, see LICENSE for details.
+#}
+{%- if pagename != "search" and builder != "singlehtml" %}
+<div id="searchbox" style="display: none" role="search">
+    <div class="searchformwrapper">
+    <form class="search" action="{{ pathto('search') }}" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false" placeholder="Search"/>
+      <input type="submit" value="{{ _('Go') }}" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+{%- endif %}