Hi jj. I am the "bad water person" Kim called for elp...sorry I didn't get free til now to respond, its kinda hectic around here lately
So, I have 2 ppm iron in my well water, but also have trace amounts of maganese. My question for you is are you sure you don't have iron as well? The two are often found together...
Maganese typically stains more blackish. I'd have expected it to have given the water a purplish hue if oxidized. Since I have iron and only had discolored water once during recovery of a black water foreclosure swamp, I might be out of my proverbial depth here though
With that grain of salt, If the maganese has oxidized, you may get purplish-black staining.
Your filtering is a good first step. But the more effective filtering should be either a two-stage reducing set of filters, or at a minimum, a 25 micron to 1 micron reducing filter.
A build up of maganese will require MORE sequestrant than typical for iron lane, so I'd make every effort to FILTER first to remve as much as possible. When you apply a sequestrant, it with put the maganese back in solution, and since its in your source water, accumulation could mean a heavy diet of sequestrant.
So, for future fill water AND right now with sme extra rigging, here's what I would try -- I'm figuring it would be worth the investment because you will later want to re-rig this system to your spigot for top ups

:
Get one, or two of the Pentek 10" filter housing:
https://www.amazon.com/Pentek-Big-Blue-Filter-Housing/dp/B00BI4HXJ8
Likewise, get either a 5 micron and then a 1 micron, OR a 25 mcron to 1 micron reducing filter if using a single housing. (I will post a link in am...gotta run right now.)
Using a small pump and hoses, connect filter(s) and send a return back to pool. In ths way, you will be "filtering" it down.
Run this in addition to your filter for a few days and see if this helps it clear.
Once clear, use a double start up of sequestrant (are you saltwater or regular chlorine pool? That will determine which type...Jacks purple for salt, or maybe metal magic for regular.)
Let me know if you have questions...I'll check back in am
