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
private final IngestDocument ingestDocument;
        IngestDocumentMatcher(String index, String type, String id, Map<String, Object> source) {
            this.ingestDocument = new IngestDocument(index, id, 1, null, null, source);
        }
        IngestDocumentMatcher(String index, String type, String id, long version, VersionType versionType, Map<String, Object> source) {
            this.ingestDocument = new IngestDocument(index, id, version, null, versionType, source);
        }
        @Override
        public boolean matches(IngestDocument other) {
            
            return Objects.equals(ingestDocument.getSource(), other.getSource())
                && Objects.equals(ingestDocument.getMetadata().getMap(), other.getMetadata().getMap());
        }
    }
    private void assertProcessorStats(int processor, IngestStats stats, String pipelineId, long count, long failed, long time) {
        assertStats(stats.getProcessorStats().get(pipelineId).get(processor).getStats(), count, failed, time);
    }
    private void assertPipelineStats(List<IngestStats.PipelineStat> pipelineStats, String pipelineId, long count, long failed, long time) {
        assertStats(getPipelineStats(pipelineStats, pipelineId), count, failed, time);
    }
    private void assertStats(IngestStats.Stats stats, long count, long failed, long time) {
        assertThat(stats.getIngestCount(), equalTo(count));
        assertThat(stats.getIngestCurrent(), equalTo(0L));
        assertThat(stats.getIngestFailedCount(), equalTo(failed));
        assertThat(stats.getIngestTimeInMillis(), greaterThanOrEqualTo(time));
    }
    private IngestStats.Stats getPipelineStats(List<IngestStats.PipelineStat> pipelineStats, String id) {