You are in metal conduit, that is where I live. All of the research you've been doing has presumed you are dealing with Romex cables that are unchangeable in the walls, you need to ignore those bits.
Even though this is new construction ~2021, I don't see a white wire bundle in this box which I thought was code.
In conduit, it's super easy to pull additional wires later, so the wire doesn't need to be installed if they leave room for it. Which they did.
However, I do see a capped purple bundle that isn't connected to either of the two existing switches. Can these wires be safely considered the neutrals in this case?
No chance of that. Purple is not a neutral color, it's another hot wire doing a task unrelated to your project.
I really can't see what's going on in this box because of a) all the white crud on the wires, and b) you didn't take a photo looking up into the pipes. If you cleaned off that white crud and took that photo I could tell you a lot more.
the other end of this 3-way switch is a dead-end 3-way switch with two blacks and one red wire.
Okay, that bodes well for your project. By the way, the building codes require you to have switches at certain entrances. Builders don't install lengthy conduit runs for their health, so most likely this switch is mandatory. No trouble though, you can eat your cake and have it too with a combo switch-receptacle. Or you could use a wireless remote with that smart switch you are adding.
Based on the above, my goal was to find a neutral in this box
See, that's you still thinking in Romex: "the wires in the walls can't be changed and I must FIND wires". No, in conduit, you put in the wires you want. It feels hard only because it's new.
By the way, in conduit there is no re-marking wires to change their function. You install the correct wires and that's it. Better hardware and lumber stores (i.e. not big-box) sell THHN by-the-foot, and if you need a color they don't have, 3M Super 33 electrical tape is sold in 10 colors anywhere for $4 (and mini 5-packs of popular colors for $6).
You generally want to use THHN solid wire, #12 is the universal donor but #14 is allowed if all the other wire is.
With metal boxes, you want to use the $3 spec grade outlets which do two nice things for you: #1 they self-ground via the mounting screws (due to a scraper brush on the screw), and #2 they use "screw-and-clamp" back-wiring which makes it possible for a novice to work with stranded wire. Your old wire might be stranded. Stranded is really better, but too difficult to put on a side screw and not legal in a backstab.