Deprecate background flag for creating indexes.

And fix type name in tests.

See #5074
Original pull request #5085

spring-data-mongodb/src/main/java/org/springframework/data/mongodb/core/index/CompoundIndex.java

@@ -152,11 +152,15 @@ public @interface CompoundIndex {
 
 	/**
 	 * If {@literal true} the index will be created in the background.
+	 * <p>
+	 * <strong>NOTE:</strong> Since MongoDB 4.2 the background flag is ignored by the server if set.
 	 *
 	 * @return {@literal false} by default.
 	 * @see <a href=
 	 *      "https://docs.mongodb.org/manual/core/indexes/#background-construction">https://docs.mongodb.org/manual/core/indexes/#background-construction</a>
+	 * @deprecated since 5.0 for removal without replacement.
 	 */
+	@Deprecated(since = "5.0", forRemoval = true)
 	boolean background() default false;
 
 	/**

spring-data-mongodb/src/main/java/org/springframework/data/mongodb/core/index/Index.java

@@ -94,10 +94,15 @@ public class Index implements IndexDefinition {
 
 	/**
 	 * Build the index in background (non blocking).
+	 * <p>
+	 * <strong>NOTE:</strong> Since MongoDB 4.2 the background flag is ignored by the server if set.
 	 *
 	 * @return this.
 	 * @since 1.5
-	 */@Contract("-> this")
+	 * @deprecated since 5.0 for removal without replacement.
+	 */
+	@Deprecated(since = "5.0", forRemoval = true)
+	@Contract("-> this")
 	public Index background() {
 
 		this.background = true;

spring-data-mongodb/src/main/java/org/springframework/data/mongodb/core/index/Indexed.java

@@ -123,11 +123,15 @@ public @interface Indexed {
 
 	/**
 	 * If {@literal true} the index will be created in the background.
+	 * <p>
+	 * <strong>NOTE:</strong> Since MongoDB 4.2 the background flag is ignored by the server if set.
 	 *
 	 * @return {@literal false} by default.
+	 * @deprecated since 5.0 for removal without replacement.
 	 * @see <a href=
 	 *      "https://docs.mongodb.org/manual/core/indexes/#background-construction">https://docs.mongodb.org/manual/core/indexes/#background-construction</a>
 	 */
+	@Deprecated(since = "5.0", forRemoval = true)
 	boolean background() default false;
 
 	/**

spring-data-mongodb/src/test/java/org/springframework/data/mongodb/core/index/MongoPersistentEntityIndexResolverUnitTests.java

@@ -670,7 +670,7 @@ public class MongoPersistentEntityIndexResolverUnitTests {
 		public void compoundIndexDoesNotSpecifyNameWhenUsingGenerateName() {
 
 			List<IndexDefinitionHolder> indexDefinitions = prepareMappingContextAndResolveIndexForType(
-					ComountIndexWithAutogeneratedName.class);
+					CompoundIndexWithAutogeneratedName.class);
 
 			IndexDefinition indexDefinition = indexDefinitions.get(0).getIndexDefinition();
 			assertThat(indexDefinition.getIndexOptions())
@@ -835,10 +835,10 @@ public class MongoPersistentEntityIndexResolverUnitTests {
 
 		class IndexDefinedOnSuperClass extends CompoundIndexOnLevelZero {}
 
-		@Document("ComountIndexWithAutogeneratedName")
+		@Document("CompoundIndexWithAutogeneratedName")
 		@CompoundIndexes({ @CompoundIndex(useGeneratedName = true, def = "{'foo': 1, 'bar': -1}", background = true,
 				sparse = true, unique = true) })
-		class ComountIndexWithAutogeneratedName {}
+		class CompoundIndexWithAutogeneratedName {}
 
 		@Document("WithComposedAnnotation")
 		@ComposedCompoundIndex