How many positions per second can the Sesse supercomputer analyze?
Obviously, it depends on the position. Since it is not running now, I relied on a Google search, and looked at some images. I am not going to post them since they are copyrighted, but you can do a Google search, and click on images, and find these in order.
In the first, a Carlsen-So game (dead link), after 49.b3, and endgame, Sesse is looking at 49,582,886/nodes per second.
In the second, Carlsen-Donchenko (players not shown in the photo), a middlegame, Sesse is looking at 17,380,039/nodes per second
In a third, Carlsen-Caruana, another endgame, but with more pieces on the board than the first example, Sesse is looking at 27,800,515/nodes per second.
In a forth, So-Carlsen, another middlegame, Sesse is looking at 15,699,501/nodes per second.
I was ready to post my answer, but then I found another one, Caruana-Carlsen, a middlegame, and Sesse is looking at 82,657,387/nodes per second!
So, you can see it really varies a lot, and depends on how complicated the position, but if you are looking for a high-end number, at least 82 million seems to be a good answer, but it could easily be higher.
Wikipedia's article on the World Chess Championship 2018 has the following line on Sesse:
The games were analysed live by the Sesse computer, running Stockfish. The computer uses a 20-core 2.3 GHz Haswell-EP CPU, which is significantly more powerful than standard computers, but not at supercomputer level.
TCEC Stockfish is currently playing with 88 cores and runs at ~200 million nodes per second. If each core contributes exactly the same amount of nps, Sesse should get about 45 million nps.
And yes, 20 cores is significantly more powerful than common personal computers, but very, very far from supercomputer level.
Monitoring Carlsen-Nepo game right now. It shows: "42,879,905,610 nodes, 203,357,230 nodes/sec, depth 58 ply (41 selective), 1,129,044 Syzygy hits" after move 11. So it's around 200M positions per sec. The HW used is also shown there at the bottom of the page: "main analysis: 200x2.0GHz Ice Lake-SP (OpenMPI), multi-PV search: 112x2.25GHz Zen 2"