Hyperthreading

I don't believe that hyperthreading on or off, will affect the latency, what can be affected is perfomance, by the way there is a extensive post of a guy who tested several cpus and showed that pianoteq only took significative advantaje from the two first physical cores, hyperthreading and more than two cores had less impact on perfomance. Thus, it is better (or was at that time) to have two fast cores than four slow ones.
If I find this post, I will paste the link here...

Edit: this is the post https://www.forum-pianoteq.com/viewtopic.php?id=4149

I am almost convinced that latency has more to do with the audio interface and drivers, the cpu power will let you have more polyphony but not less latency. I did not find significative difference in latency between an AMD Turion M500 Intel Pentium 2020m. I've lost my latency measurements, but the Intel was newer and faster, latency was about the same.
I don't know how familiar are you with maths but latency could be predicted quite accurately by the following equation:
latency= 3*(pianoteq shown latency) + 4ms
or something like this, where pianoteq shown latency is what you read when configuring the buffer size, and frequency (pianoteq shown latency= buffer size/samplerate). I'm sure about the slope 3 but not the intercept, anyway it wasn't much different between those two processors. Those measurements were made recording on a channel pianoteq sound and on the other the digital piano sound, then measuring the distance between the two sounds, very similar to what you did. Driver was ASIO4all and the sound was generated in the internal sound card. USB sound card had much worse performance.
Now I own a much better laptop, if you are courious I can measure and see how it compares (if I find old measurements)

Not to doubt the results of your experiment, but I think the methodology could use improvement

According to what else was running and what else had run recently - the first measurement could have been slowed by other tasks/processes and or their residue.
The second experiment started on a relatively "clean" machine.

I would therefore do both experiments several times on clean re-boots.
There is still likely to be variation, something you can ponder.

So with hyperthreading turned ON the two lowest latency measurements were 13 and 14 ?
with it OFF they were 13 and 16 ?

I was just imagining what if Modartt could design/update a new sond engine for a processor like this :

https://www.amazon.com/Intel-i9-9980XE-...amp;sr=8-7

18 cores of 4,4ghz each...
36 threads...

They would be able compute much more details for ultra hyper realistic sounds.

Yes, if the software core sound generator do not get redesign for ultra fast processors, only the latency will change.
That's why I said that to work it's require redesign the software core sound generator to allow more precision for extra calculation.  But it's just a idea, since at the moment the public with such processors are not enought to justify such investment.

I was one of the first, if not the first, to imagine and suggest to use non-real time calculation (audio export for example) to make pianoteq use a lot more calculation, more precision, to create perfect piano sounds up to the point to shut-up any critic. Studios, for example, could play the piano in real time( while the artist performs) and later render it using algorithms that requires heavier computation to produce perfect piano sounds. Even if took 1 hour to render 5 minutes of performance, it would be worthwhile.

The problem it's the high cost to redesign the software core sound generator. Other problem is that people could get used with the perfect sound rendered and start to spot/point more deffects in the real time playing mode. But today pianoteq 6.5 it's already very good, close to the real thing.