Several years ago, I had a sand filter and relied on bad pool store info.
I had a point where my pool looked like your last pic. I was told to vacuum, so I did. All the algae straight into the filter. I fought a similar battle that you are going through with only input from the pool store who sold me droves of stuff on their recommendation. Their final solution was that my sand must have gone bad.
When I went to replace the sand, the top several inches were pure dark green. Looked like spinach. There was so much algae, I could never get ahead of it. It would never backwash out.
I replaced the sand, fired back up and things finally straightened out. In retrospect, if I had vacuumed to waste when I had all the visible algae, I probably could've avoided a lot of headache and wasted money.
Morale of the story to me was if I see algae, I get it out of the pool, not into the filter.
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