Simplify logic around missing shards check in search phases

This removes a couple of indirections: the error message for missing shards is always the
same no matter the search phase. This was required to provide a slightly different error
message for open PIT. The previous error was misleading when open PIT did not support
setting allow_partial_search_results, but now that it does, it looks like we can unify
the error message and simplify the code around it.

Author: javanna

server/src/internalClusterTest/java/org/elasticsearch/search/retriever/RetrieverRewriteIT.java

@@ -127,7 +127,10 @@ public void testRewriteCompoundRetrieverShouldThrowForPartialResults() throws Ex
                 SearchPhaseExecutionException.class,
                 client().prepareSearch(testIndex).setSource(source)::get
             );
-            assertThat(ex.getDetailedMessage(), containsString("Search rejected due to missing shards"));
+            assertThat(
+                ex.getDetailedMessage(),
+                containsString("Search rejected due to missing shards")
+            );
         } finally {
             internalCluster().restartNode(randomDataNode);
         }

x-pack/plugin/sql/qa/server/single-node/src/javaRestTest/java/org/elasticsearch/xpack/sql/qa/single_node/JdbcShardFailureIT.java

@@ -89,7 +89,7 @@ public void testPartialResponseHandling() throws Exception {
         createTestIndex();
         try (Connection c = esJdbc(); Statement s = c.createStatement()) {
             SQLException exception = expectThrows(SQLException.class, () -> s.executeQuery("SELECT * FROM test ORDER BY test_field ASC"));
-            assertThat(exception.getMessage(), containsString("[open_point_in_time] action requires all shards to be available"));
+            assertThat(exception.getMessage(), containsString("Search rejected due to missing shards"));
         }
     }