[DOCS] Move min_score docs to search API page (#60895) (#60897)

Reformats the `min_score` docs as a param definition on the
search API reference page.

Author: jrodewig

docs/reference/redirects.asciidoc

@@ -83,7 +83,7 @@ See <<inner-hits>>.
 
 [role="exclude",id="search-request-min-score"]
 === Minimum score parameter for request body search API
-See <<request-body-search-min-score>>.
+See <<search-api-min-score>>.
 
 [role="exclude",id="search-request-named-queries-and-filters"]
 === Named query parameter for request body search API
@@ -1013,6 +1013,10 @@ See <<how-es-highlighters-work-internally>>.
 === Inner hits
 See <<inner-hits>>.
 
+[role="exclude",id="request-body-search-min-score"]
+=== `min_score`
+See <<search-api-min-score>>.
+
 [role="exclude",id="request-body-search-queries-and-filters"]
 === Named queries
 

docs/reference/search/request-body.asciidoc

@@ -130,7 +130,10 @@ include::request/index-boost.asciidoc[]
 
 See <<inner-hits>>.
 
-include::request/min-score.asciidoc[]
+[[request-body-search-min-score]]
+==== `min_score`
+
+See <<search-api-min-score>>.
 
 [[request-body-search-queries-and-filters]]
 ==== Named queries

docs/reference/search/request/min-score.asciidoc

@@ -326,6 +326,12 @@ As an alternative to deep paging, we recommend using
 <<search-after,`search_after`>> parameter.
 --
 
+[[search-api-min-score]]
+`min_score`::
+(Optional, float)
+Minimum <<relevance-scores,`_score`>> for matching documents. Documents with a
+lower `_score` are not included in the search results.
+
 [[request-body-search-query]]
 `query`::
 (Optional, <<query-dsl,query object>>) Defines the search definition using the