There's a little buglet in #85387 (which was the PR that closed #84046), specifically, it doesn't account for the possibility that there's both a default/request **and** and a final pipeline, and that they can both touch the `@timestamp` field.

`IngestService#postIngest` was added in #85387, and it's intended that the logic there only runs **once**, after all the pipelines associated with the request have been executed. But as it's currently written, the logic actually runs after each individual pipeline runs.

The consequence of that is that if there's a default/request and a final pipeline in use for a document, and the final pipeline changes the timestamp field, the `rawTimestamp` recorded for the `IndexRequest` associated with the document will mistakenly use the value it sees after the default/request pipeline runs, and **not** the most correct one (from after when the final pipeline runs).

/cc @martijnvg 
server/src/test/java/org/elasticsearch/ingest/IngestServiceTests.java
String value = (String) config.remove("value");
            if (externalProperty[0]) {
                return new FakeProcessor("set", tag, description, (ingestDocument) -> ingestDocument.setFieldValue(field, value));
            } else {
                return new AbstractProcessor(tag, description) {
                    @Override
                    public IngestDocument execute(IngestDocument ingestDocument) throws Exception {
                        throw new RuntimeException("reload me");
                    }
                    @Override
                    public String getType() {
                        return "set";
                    }
                };
            }
        });
        IngestService ingestService = createWithProcessors(processorFactories);
        ClusterState clusterState = ClusterState.builder(new ClusterName("_name")).build();
        ClusterState previousClusterState = clusterState;
        PutPipelineRequest putRequest1 = new PutPipelineRequest("_id1", new BytesArray("""
            {"processors": [{"set" : {"field": "_field", "value": "_value", "tag": "tag1"}}]}"""), XContentType.JSON);
        clusterState = executePut(putRequest1, clusterState);
        ingestService.applyClusterState(new ClusterChangedEvent("", clusterState, previousClusterState));
        {
            Exception[] exceptionHolder = new Exception[1];
            IngestDocument ingestDocument = RandomDocumentPicks.randomIngestDocument(random(), new HashMap<>());
            ingestService.getPipeline("_id1").execute(ingestDocument, (ingestDocument1, e) -> exceptionHolder[0] = e);
            assertThat(exceptionHolder[0], notNullValue());
            assertThat(exceptionHolder[0].getMessage(), containsString("reload me"));
            assertThat(ingestDocument.getSourceAndMetadata().get("_field"), nullValue());