Based on my own testing of the issue, it seems that the moving block is controlled by the piston that moved it. (Discovered by cloning the moving block somewhere else while being moved. It doesn't revert to a regular block when movement finishes, and extending/retracting the piston that created it causes it to move, no matter how far away it is. Destroying the piston causes it to revert to a regular block where it should have reverted to earlier.)
Based on that, I think that what is actually occurring here is that the reverting of the moving block is done during the step of updating the piston that moved it, so the issue is the same as MCPE-16371. The solution here is to have pistons finishing movement always updated before pistons starting movement. There is already a feedback suggestion on that fix.
Interestingly, I have actually managed to implement this fix using commands, by destroying and then replacing the piston midway through movement, which makes the moving blocks revert faster than they are supposed to. This also provides more evidence that the moving blocks are controlled by the piston that created them.
I noticed some similar posts about blocks having strange mixed solid/non-solid properties, so I decided to test some of the solid/non-solid properties of most blocks in the game, and I found many more that have strange solid/non-solid properties, a total of 25, but there may be some I missed. Some of these properties are useful, namely the cutting of redstone lines by copper bulbs and comparators reading signals through pistons, and I think those should be kept. I think the posts should be set up to be one post per strange solid/non-solid behavior, ie "visuals of redstone line being cut/not cut don't match behavior" should be one post, "comparators reading/not reading signals through blocks they shouldn't/should" should be another post, and "minecarts not bouncing off of blocks they should" should be another post. Each post would list the bocks affected.
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This setup can actually detect if you are just standing near any redstone inputs anywhere in the world. Very strange.