[DOCS] Fix `search_timeout` parameter docs (#66075)

Co-authored-by: James Rodewig <40268737+jrodewig@users.noreply.github.com>

docs/reference/docs/delete-by-query.asciidoc

@@ -213,7 +213,10 @@ include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=scroll_size]
 
 include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=search_type]
 
-include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=search_timeout]
+`search_timeout`::
+(Optional, <<time-units, time units>>)
+Explicit timeout for each search request.
+Defaults to no timeout.
 
 include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=slices]
 

docs/reference/docs/update-by-query.asciidoc

@@ -213,7 +213,10 @@ include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=scroll_size]
 
 include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=search_type]
 
-include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=search_timeout]
+`search_timeout`::
+(Optional, <<time-units, time units>>)
+Explicit timeout for each search request.
+Defaults to no timeout.
 
 include::{es-repo-dir}/rest-api/common-parms.asciidoc[tag=slices]
 

docs/reference/rest-api/common-parms.asciidoc

@@ -783,13 +783,6 @@ tag::search-time-ms[]
 The amount of time spent searching, in milliseconds.
 end::search-time-ms[]
 
-tag::search_timeout[]
-`timeout`::
-(Optional, <<time-units, time units>>)
-Explicit timeout for each search request.
-Defaults to no timeout.
-end::search_timeout[]
-
 tag::search-total[]
 The number of search operations on the source index for the {transform}.
 end::search-total[]