Had the same thing happen a couple of springs ago, brownish blotches mostly near the deep end. I didn’t drain the pool, but what helped me was lowering the chlorine a bit first, then trying a vitamin C tablet pressed directly on one of the stains. Weird trick, but it told me right away it was metal-related, not organic.
Once I knew that, I used a metal stain remover made for filled pools and let it circulate for a full day. The stains didn’t vanish instantly, but by the next morning, most had faded way down. I followed up by running the filter a little longer than usual and brushing daily for a few days.
Didn’t damage anything, and I didn’t have to mess with draining, which was a win.