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

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

docs/reference/redirects.asciidoc

@@ -89,7 +89,7 @@ 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
@@ -1020,6 +1020,10 @@ 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

@@ -1,19 +0,0 @@
-[[request-body-search-min-score]]
-==== min_score
-
-Exclude documents which have a `_score` less than the minimum specified
-in `min_score`:
-
-[source,console]
---------------------------------------------------
-GET /_search
-{
-  "min_score": 0.5,
-  "query" : {
-    "term" : { "user" : "kimchy" }
-  }
-}
---------------------------------------------------
-
-Note, most times, this does not make much sense, but is provided for
-advanced use cases.

docs/reference/search/search.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