Your corals didn't look dead or bleached by any measure, FWIW.
They had their polyps contracted, but in the pics you attached, the birdsnest and montipora colony looked stressed but not bleached. Though your birdsnest colony was bleached white on the inside, which is more a function of not enough flow getting to it in normal day-to-day operations, not a function of anything you did in your sump.
The refugium looked nasty, but that's okay, that's what it is there for. The messier your sump, oftentimes the cleaner your display will be. I would just siphon off those dianoflagellates and any cyano in the sump, and ideally replace the caulerpa with some Chaeto, and then just let it do it's growing thing. I would even make sure to add extra flow in there so nothing settles, and it tumbles the chaeto (not necessary, but ideal for increased growth).
Though you could just let crud settle in there which makes it easier to siphon out. That's how my biocube is set up. High flow in the display makes detritus settle only in the low-flow sump, which is easy and an ideal location for me to siphon it out again later.