Q: At the end of a turn, which would happen first: the Holographic Projector/Holodeck turns off, or Keepers are discarded from a Keeper Limit?

…One player would have been winning on their turn due to the Holographic Projector imitating another Keeper, except that they also had a Keeper-With-Attached-Creeper. At the end of their turn, the Keeper Limit compelled them to discard a Keeper, and they discarded the one with the Creeper, so they were no longer prevented from winning… but was it no longer their turn, so the Holographic Projector was no longer imitating the other required Keeper?

A: In this case those two things are considered to happen simultaneously: the discard of the Creeper (via the Keeper Limit) and the “turning off” of the Holographic Projector. Execute both things, and THEN evaluate whether anyone is meeting the win conditions. That player essentially goes instantaneously from not-winning because of the Creeper, to not-winning because their Hologram isn’t working. A sad story for them.