You are correct .. none of the old publishing pipelines are called when the new service is installed.
Traditionally, Sitecore publishes one item at a time. This is inefficient at a larger scale so the
Publishing Service, instead, processes items in batches.
This means the existing pipelines are no longer conceptually compatible so there needed to be a 'batched' way of accessing the changes generated from a publish operation.
At the end of a publish, the
Publishing Service will push all 'manifest results' (i.e changes that have just have just published) in batches to a pipeline.
args object of this pipeline contains all items have that been created / updated / deleted during the publish process but before the caches have been cleared.
So if you need to check that certain types of item have been published or need to log anything extra or make any other changes then this pipeline is the place to do it.
Sitecore handles the batching and loading for you, you just process the batches as part of the pipeline arguments.
The pipeline you need to look at the
PublishBatchResult pipeline (found as part of the Sitecore Module in
App_Config\Include\Sitecore.Publishing.Service.config - rather than the Publishing Service itself).
From the config:
This pipeline is called from publishingservice:publishend event handler which subscribes to the publish end event. Publish results will
be passed to this pipeline in batches. The size of the batch is defined by 'manifestResultLoadBatchSize' parameter specified within
the publishingservice:publishend configuration section.
If you create a processor in here you will receive a
PublishEndResultBatchArgs object which will contain a batch of
ManifestOperationResult<ItemResult> objects from which you can interrogate and some other helpful properties.
As mentioned, you can adjust the size of these batches in the config.
Sitecore uses this pipeline to issue the events that clear the caches on the CD servers .. so putting your processor before this means your processor will get called before the cache clear, afterwards is gets called after the cache clear.