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> I guess the question is whether rsync is using multiple threads or otherwise accessing the filesystem in parallel

No, that is not the question. Even Wikipedia explains that rsync is single-threaded. And even if it was multithreaded "or otherwise" used concurent file IO:

The question is whether rsync _transmission_ is pipelined or not, meaning: Does it wait for 1 file to be transferred and acknowledged before sending the data of the next?

Somebody has to go check that.

If yes: Then parallel filesystem access won't matter, because a network roundtrip has brutally higher latency than reading data sequentially of an SSD.

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Note that rsync on many small files is slow even within the same machine (across two physical devices), suggesting that the network roundtrip latency is not the major contributor.
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