[DOCS] Add template docs to scripts. Reorder template examples. (#45817)

* [DOCS] Add template docs to scripts. Reorder template examples.

* Adds a 'Search template' section to the 'How to use scripts' chapter.
  This links to the 'Search template' chapter for detailed info and
  examples.

* Reorders and retitles several examples in the 'Search template'
  chapter. This is primarily to make examples for storing, deleting, and
  using search templates more prominent.

* Change <templatename> to <templateid>

Author: jrodewig

docs/reference/scripting/using.asciidoc

@@ -195,6 +195,21 @@ DELETE _scripts/calculate-score
 // CONSOLE
 // TEST[continued]
 
+[float]
+[[modules-scripting-search-templates]]
+=== Search templates
+You can also use the `_scripts` API to store **search templates**. Search
+templates save specific <<search-search,search requests>> with placeholder
+values, called template parameters.
+
+You can use stored search templates to run searches without writing out the
+entire query. Just provide the stored template's ID and the template parameters.
+This is useful when you want to run a commonly used query quickly and without
+mistakes.
+
+Search templates use the http://mustache.github.io/mustache.5.html[mustache
+templating language]. See <<search-template>> for more information and examples.
+
 [float]
 [[modules-scripting-using-caching]]
 === Script caching