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/main/java/org/elasticsearch/ingest/IngestService.java
private final List<Consumer<ClusterState>> ingestClusterStateListeners = new CopyOnWriteArrayList<>();
    private volatile ClusterState state;
    /**
     * Cluster state task executor for ingest pipeline operations
     */
    static final ClusterStateTaskExecutor<PipelineClusterStateUpdateTask> PIPELINE_TASK_EXECUTOR = batchExecutionContext -> {
        final var allIndexMetadata = batchExecutionContext.initialState().metadata().indices().values();
        final IngestMetadata initialIngestMetadata = batchExecutionContext.initialState().metadata().custom(IngestMetadata.TYPE);
        var currentIngestMetadata = initialIngestMetadata;
        for (final var taskContext : batchExecutionContext.taskContexts()) {
            try {
                final var task = taskContext.getTask();
                try (var ignored = taskContext.captureResponseHeaders()) {
                    currentIngestMetadata = task.execute(currentIngestMetadata, allIndexMetadata);
                }
                taskContext.success(() -> task.listener.onResponse(AcknowledgedResponse.TRUE));
            } catch (Exception e) {
                taskContext.onFailure(e);
            }
        }
        final var finalIngestMetadata = currentIngestMetadata;
        return finalIngestMetadata == initialIngestMetadata
            ? batchExecutionContext.initialState()
            : batchExecutionContext.initialState().copyAndUpdateMetadata(b -> b.putCustom(IngestMetadata.TYPE, finalIngestMetadata));
    };
    /**
     * Specialized cluster state update task specifically for ingest pipeline operations.
     * These operations all receive an AcknowledgedResponse.
     */
    public abstract static class PipelineClusterStateUpdateTask implements ClusterStateTaskListener {