With the most recent Syl interlude, we seemingly got confirmation that shardplate is made up of spren. Syl specifically refers to shardplate as being made up of lots of corpses. One of the major questions that arises from this is how the shardplate is able to regenerate from stormlight if it's made up of corpses. The following is my theory of how that happens.
I believe the clue to understanding how shardplate regenerates lies in the existence of deadeyes. We know that each shardblade has a cognitive aspect whose sole purpose is to follow around the human carrying their blade. Why wouldn't shardplate have a similar cognitive aspect or aspects? I believe that shardplate has some group of cognitive beings that function similarly to the deadeyes and correspond to the various corpses in the plate. Each cognitive corpse follows around the piece of plate they correspond to.
When plate is broken. the cognitive corpses continue to follow around the part of the plate they correspond to. The various spren that made up the plate, however, are Connected. Feeding stormlight to the plate essentially does two things. First, it uses the Connections between the spren to draw their cognitive aspects to the same location in the Cognitive Realm. Maybe by making the Connections between the spren temporarily stronger than the Connection with the physical piece of plate or just making them want to come get food. Once the spren are all in the same location in the Cognitive Realm, the stormlight allows the spren to use their Connection with the spren already in the Physical Realm at that location to reform there as plate. When multiple pieces get stormlight at the same time, the larger one contains more spren and therefore a stronger Connection to the group of spren as a whole.
This explanation probably needs some tweaks but I think it uses what we know of how plate and blades work to create a relatively simple yet Realmatically viable answer. I'd love feedback on what others think of this theory and if they have any tweaks on how they think this could work.