[Rest Api Compatibility] content-type headers are not vendor specific when exception is returned

[pgomulka]

Elasticsearch Version

8.5

Installed Plugins

No response

Java Version

bundled

OS Version

macos

Problem Description

when an exception like 404 not found is returned a response content type is not vendor specific even though the Accept header was vnd specific on a request.

Steps to Reproduce

send a request to a non existing index
curl -k --request GET -u elastic:f2RROKkV5m_2P+VCMYdU --url https://localhost:9200/missing/_search --header 'Content-Type: application/vnd.elasticsearch+json;compatible-with=8' --header 'Accept: application/vnd.elasticsearch+json;compatible-with=8' -v

response
< HTTP/1.1 404 Not Found
< X-elastic-product: Elasticsearch
< content-type: application/json;charset=utf-8
< content-length: 371
<

• Connection #0 to host localhost left intact
  {"error":{"root_cause":[{"type":"index_not_found_exception","reason":"no such index [missing]","resource.type":"index_or_alias","resource.id":"missing","index_uuid":"na","index":"missing"}],"type":"index_not_found_exception","reason":"no such index [missing]","resource.type":"index_or_alias","resource.id":"missing","index_uuid":"na","index":"missing"},"status":404}%

I think this is due to error handling was not implemented fully with rest api compatibility project.
the fix should change

elasticsearch/server/src/main/java/org/elasticsearch/rest/RestResponse.java

Line 125 in 06d4ef7

this.responseMediaType = builder.contentType().mediaType();

--- a/server/src/main/java/org/elasticsearch/rest/RestResponse.java
+++ b/server/src/main/java/org/elasticsearch/rest/RestResponse.java
@@ -122,7 +122,7 @@ public class RestResponse {
         try (XContentBuilder builder = channel.newErrorBuilder()) {
             build(builder, params, status, channel.detailedErrorsEnabled(), e);
             this.content = BytesReference.bytes(builder);
-            this.responseMediaType = builder.contentType().mediaType();
+            this.responseMediaType = builder.getResponseContentTypeString();
         }

Logs (if relevant)

No response

[elasticsearchmachine]

Pinging @elastic/es-core-infra (Team:Core/Infra)

[pgomulka]

a similar problem occurs in EQL
extracted this comment to a new issue #92710