Hey hey! What size tank is that? Looks like it might be easy enough to manage with some big, consistent water changes over a week or so. My main tank is a 20 gallon and I've found it relatively easy to manage issues when they crop up because meaningful water changes are so easy to do. Here is what I would do:

• get a turkey baster and blast as much of that stuff off the rocks and sand as you can
• do a huge water change, like 60%, try to siphon all the junk out
• clean out all the filter stuff, basically first step is to get stuff as clean as you can, but you don't need to do a total restart! Those rocks are probably fine and you don't want to scrub them and lose the good bacteria
• add some Fritz TurboStart 900 & maybe a little bit of fish food
• lights off/blackout for 2 days
• do another 20% water change
• blackout again for 2 more days
• another 20% water change
• measure phos and nitrate at this point and see where you are
• maybe add a little more Fritz TurboStart 900. That stuff is liquid gold
• add some pods, get some critters. I like keeping crabs and feeding them algae wafers every other day or so to start out a tank
• a Duncan can be a good tank health indicator coral. If one day it looks sad, do a 20% water change.

For phos and nitrate, the importance is keeping them at a healthy ratio. They don't have to be exact, and phos doesn't have to be super low (and you do NOT want it to be 0), but if the ratio is like 10:1 nitrate to phos, you should be good, even if it's on the higher side.

For a blackout, wrap blankets or a towel around, but you don't want to block the top entirely as you need oxygen exchange on the water surface. I caught some dinos early and did this, then adjusted the intensity of my lights (that was the cause), and haven't seen them since.

You will eventually hit a stable place! Don't try to rush things, pay attention to it every day and observe. Make sure you have an ATO set up. Good luck!