_mvt endpoint does not include cross cluster prefix with `_index` value. For example, `_index` returns `myIndexPattern` instead of expected `cluster_one:myIndexPattern`. _search endpoint includes cross cluster prefix with `_index` value. This is causing problems in [Kibana maps tooltips](https://github.com/elastic/kibana/issues/153210)
x-pack/plugin/vector-tile/qa/multi-cluster/src/javaRestTest/java/org/elasticsearch/vectortile/VectorTileCCSIT.java
@Override
    protected Settings restClientSettings() {
        final String token = basicAuthHeaderValue("admin", new SecureString("admin-password".toCharArray()));
        return Settings.builder().put(ThreadContext.PREFIX + ".Authorization", token).build();
    }
    private int createIndex(RestClient client, String indexName) throws IOException {
        final Request createRequest = new Request(HttpPut.METHOD_NAME, indexName);
        Response response = client.performRequest(createRequest);
        assertThat(response.getStatusLine().getStatusCode(), Matchers.equalTo(HttpStatus.SC_OK));
        final Request mappingRequest = new Request(HttpPut.METHOD_NAME, indexName + "/_mapping");
        mappingRequest.setJsonEntity("""
            {
              "properties": {
                "location": {
                  "type": "geo_shape"
                }
              }
            }""");
        response = client.performRequest(mappingRequest);
        assertThat(response.getStatusLine().getStatusCode(), Matchers.equalTo(HttpStatus.SC_OK));
        final Request putRequest = new Request(HttpPost.METHOD_NAME, indexName + "/_doc");
        putRequest.setJsonEntity("{\"location\": \"POINT(0 0)\"}");