Dovahklon did such a good job figuring out this problem for Skyrim (and explaining it) that I have went ahead and re-created her mod for Fallout 4 and included most of the original description below (corrections added for Fallout 4's values).

Have you ever wonder why the NPCs mostly just stay at the same floor, even though the cell (regardless where at) has multiple floors?

Do you have a nice custom home that has multiple floors in the same cell(i.e. no loading doors), and you want your NPCs to move up and downstairs more?

This little tweak should address that need.

What does sandboxing mean?
Sandboxing is just a term describing NPCs' auto behavior in a given location, like walking around, sitting down, drinking, eating, etc. Keep in mind that NPCs cannot roam outside of this location.

Why don't NPCs go up and down the floors in a cell (a single loaded area) with multiple floors?
In Skyrim, NPC's sandboxing behaviors are defined to a specific location in 3d (a spherical shape). The global game settings GMST fSandboxCylinderTop and fSandboxCylinderBottom restricts that location to a more flat shape (imagine chopping the top and bottom of an orange off, so it's flat on top and bottom). The default value for fSandboxCylinderTop is 150 and fSandboxCylinderBottom -50, which is too flat for the NPC to notice things the floor above or below (a floor is 288 unit tall).

What this does:
This is a little tweak to change the global game settings GMST fSandboxCylinderTop from 150 to 576, and fSandboxCylinderBottom from -50 to -576. As a result, the NPC can detect things (markers for various actions) roughly 2 floors above and below during their sandboxing behavior within their sandbox radius, so they will go up or down the floors to use those things (furnitures, markers, etc.).

Requirements:
None, just Fallout 4 the base game.

Compatibility:
Should be compatible to everything.

How to Install:
NMM: simply download with NMM and install it with NMM

Manual Install: simply extract Multiple Floors Sandboxing.esp to Fallout 4\Data

Load order doesn't matter. You can place it anywhere within your mod list, as I have yet know of any mods that make the same changes.

This plugin only makes small changes to the game setting. So it is entirely safe to add or remove this plugin at any point of the game. Disabling this plugin will not corrupt your playthroughs or saves.

This plugin will NOT impact game performance negatively.