I need to place several copies of these red beads into the compartment, aligning them to the floor and the walls. Once I align the first two, I will pile copies of them (easy task, so no need for this) and then make other copies, vertically rotated by 90° (around x or y axis) to fit the blank space and figure out how many can be placed without overlapping or “brimming over”. It should be pretty easy if I can stop their translation when there is a contact between visible surfaces (or a 3D snap of sort), but without such feature looks like an impossibly long task. Has the community found a decent workaround for this kind of tasks?
Your case is 2D challenge. Red items are expected be on one plane and aligned. I would play with sketch constrains to pack of 2 or how much you need sets of these shapes into smaller area first to create first small pattern, then translate pattern to larger area by copy translate. You will need a lot dimensions, constrains and additional construction geometries.
In 3D also additional sketch will help to align models.