[DOCS] Remove incorrect parms from put index template API docs (#53750)

Removes the `flat_settings` and `timeout` query parameters from the JSON
spec and asciidoc docs for the put index template API.

These parameters are not supported by the API.

docs/reference/indices/templates.asciidoc

@@ -93,10 +93,6 @@ Name of the index template to create.
 If `true`, this request cannot replace or update existing index templates.
 Defaults to `false`.
 
-include::{docdir}/rest-api/common-parms.asciidoc[tag=flat-settings]
-
-include::{docdir}/rest-api/common-parms.asciidoc[tag=include-type-name]
-
 `order`::
 (Optional,integer)
 Order in which {es} applies this template
@@ -106,7 +102,7 @@ Templates with lower `order` values are merged first.
 Templates with higher `order` values are merged later,
 overriding templates with lower values.
 
-include::{docdir}/rest-api/common-parms.asciidoc[tag=timeoutparms]
+include::{docdir}/rest-api/common-parms.asciidoc[tag=master-timeout]
 
 
 [[put-index-template-api-request-body]]

rest-api-spec/src/main/resources/rest-api-spec/api/indices.put_template.json

@@ -36,17 +36,9 @@
         "description":"Whether the index template should only be added if new or can also replace an existing one",
         "default":false
       },
-      "timeout":{
-        "type":"time",
-        "description":"Explicit operation timeout"
-      },
       "master_timeout":{
         "type":"time",
         "description":"Specify timeout for connection to master"
-      },
-      "flat_settings":{
-        "type":"boolean",
-        "description":"Return settings in flat format (default: false)"
       }
     },
     "body":{