As far as the shaft goes, it might look sloppy, but it’s built to specifications. Noise is noise and attempting to mitigate it is an ambitious desire. I’m certain nothing will happen on the “shaft side” as far as soundproofing goes due to cost on your part.
Some might suggest after you exhaust all outside shaft options, would be to remove all the wallboard in your unit that abuts the shaft including attic open spaces and the spaces adjacent to lobby/stairwell area in your unit and add any soundproofing materials you desire or what might be recommended by a soundproofing specialist. And the seller never thought to disclose this nuisance noise. Hmmm.
Talk to the tenant just below you. Do they hear what you hear? Is the noise that annoying to them?
Remember, based on your earlier photos, the top floor is an echo chamber.