Minecraft wiki entry for Shulker_Box, associated text: With 37 shulker boxes in a player's inventory, hotbar, and off-hand slot, 999 stacks of up to 64 items (up to 63,936 total items; 63,973 if counting shulker boxes themselves) can be held. With 37 shulker boxes and an ender chest with 27 shulker boxes in one of the shulker box slots, 1,727 stacks (up to 110,528 items; 1,728 stacks with up to 110,592 items if counting stacked ender chests) can be held.
When the camera is far enough from a shulker box, the shulker box is invisible, even though it is still within the render distance, this is because the shulker box is still considered a mob.