Is God's withholding of a particular provision from a servant due to their sins, or a trial to test their faith, or a mercy by withholding what might be a tribulation, or because they did not take sufficient means?

All the sins mentioned, God's protection of His servant, and the servant's shortcomings in pursuing means, can be a reason for the prevention of sustenance. It is not possible to definitively pinpoint the exact reason, as the matter is of the unseen. What is required by the Sharia (definition) is patience, repentance, exerting effort in pursuing means, and reliance on God, not merely knowing the reason.