Thanos in MCU is generally portrayed as not a dark villian but little bit different villain. At the very least, he views himself as a hero, albeit a hero who has to do the hard work, take hard decisions that others lack the courage to do so. Being his primary objective is bring back balance to the universe, he avoids killing people unless he feels he has no other choice. He just wants to save the dying universe by any means necesary as he sees fit.
In the scene at the Asgardian ship, he just annhilated half of the asgardians, with weaken Thor and Loki comes up. Thanos seeks the stone from Loki by further touturing Thor. Then Loki tries to kill Thanos by letting out Hulk and later by himself. Thanos killed Loki because at first he professed his undying loyalty towards Thanos but then immediately after tried to kill Thanos. For that reason, Loki kills Thanos.
Thor didn't do such a thing and Maw has already made him imprisoned inside some metallic bond. Thor was almost beaten down in the fight for saving Asgardians. In the first few scenes we saw Thanos dragging Thor by his head just like a ragdoll.
Being all that, Thanos has no evidence to believe that Thor would be any problem for his quest, he felt no threat from Thor. So Thanos felt no need to kill Thor, but just ignore him.
Before leaving the ship, Thanos used his power stone to blow up the ship and blow left ship in dissolved state, Thor would've been disintegrate with the ship, We later see that blow wasn't enough to just Kill thor at the moment, but it would be a different story if Guardians didn't help out Thor.
You mentioned It is strange that we see the Power Stone take over every bit of the ship except for what seems like a small area around Thor.. I think it was the dramatic expression of stranded Thor, who lost everything, lies helpless inside a ship which moments away from blowing upto oblivion. which shows the viewer how much helpless Thor at the time and how much powerful Thanos actually is.. he is unlike any other villian neither Thor or Avengers ever met yet.
You also mentioned Is the Power Stone helping Thor? The Power Stone blows up the ship all around Thor, so Thanos leaves assuming Thor is dead, when in fact he’s not..., Power stone couldn't help Thor. It was under the control of Thanos. We never see any connection between Thor and the power stone to ellaborate this kind of theory.
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