Ok, for some reason viewing pics on my phone, I thought the debris was in the skimmer baskets and not the pump basket...my error. If that is the case, then these are definitely plaster pieces...there's no way anything of that size could be sucked into the drains., then the pump basket.
The OP said she was vacuuming via skimmer [that would cause a suction to pull the debris thru pipes and into pump basket. Anything dumped into the pool or skimmer baskets by pool guy would not be transported into pump basket unless they vacuumed too....pucks don't break that easy and neither does gunite, but saturated plaster would,,,,my only reservation is the quantity of the debris...that's A LOT of residual material in the pipes...I had one or 2 chunks that finally ended up in my scupper pump basket...it was also the color of my pebble tec. Has the OP stated what color is the plaster? If the same or near color, that's the material...