[Inference API] Add ElasticInferenceServiceDenseTextEmbeddingsServiceSettings to InferenceNamedWriteablesProvider (#138484)

Needed for correct type identification during deserialization

Author: timgrein

docs/changelog/138484.yaml

@@ -0,0 +1,6 @@
+pr: 138484
+summary: "[Inference API] Add `ElasticInferenceServiceDenseTextEmbeddingsServiceSettings`\
+  \ to `InferenceNamedWriteablesProvider`"
+area: Machine Learning
+type: bug
+issues: []

x-pack/plugin/inference/src/main/java/org/elasticsearch/xpack/inference/InferenceNamedWriteablesProvider.java

@@ -74,6 +74,7 @@
 import org.elasticsearch.xpack.inference.services.custom.response.SparseEmbeddingResponseParser;
 import org.elasticsearch.xpack.inference.services.deepseek.DeepSeekChatCompletionModel;
 import org.elasticsearch.xpack.inference.services.elastic.completion.ElasticInferenceServiceCompletionServiceSettings;
+import org.elasticsearch.xpack.inference.services.elastic.densetextembeddings.ElasticInferenceServiceDenseTextEmbeddingsServiceSettings;
 import org.elasticsearch.xpack.inference.services.elastic.rerank.ElasticInferenceServiceRerankServiceSettings;
 import org.elasticsearch.xpack.inference.services.elastic.sparseembeddings.ElasticInferenceServiceSparseEmbeddingsServiceSettings;
 import org.elasticsearch.xpack.inference.services.elasticsearch.CustomElandInternalServiceSettings;
@@ -879,5 +880,14 @@ private static void addElasticNamedWriteables(List<NamedWriteableRegistry.Entry>
                 ElasticInferenceServiceRerankServiceSettings::new
             )
         );
+
+        // Dense Text Embeddings
+        namedWriteables.add(
+            new NamedWriteableRegistry.Entry(
+                ServiceSettings.class,
+                ElasticInferenceServiceDenseTextEmbeddingsServiceSettings.NAME,
+                ElasticInferenceServiceDenseTextEmbeddingsServiceSettings::new
+            )
+        );
     }
 }