Ok I went through a bit of the build, don't have the time for it all right now. I do have some thoughts.
First, good build and looks great. You did well.
Second, would I be correct to assume you used all dry rock? What have you added to the system to seed it or increase biodiversity? What kind of pod population do you have? Pods are the best clean up crew. The graze on everything ,except macro algae, and support the food chain in the system. Buy a pod package with several types from AlgaeBarn like others suggested and the phyto. The phyto will help support the pods reproduction and build up a happy population. Once it's gone don't bother getting more, you will see them decrease but they are now established and will reproduce and maintain on their own. Other way to boost bio diversity is get some chaeto for that fuge. Other local reefers, online, LFS, or whatever. The more sources you can collect the better. You can also buy a small live rock from an established system, try collecting a few of these and add to the bottom of the fuge (best) or anywhere in the sump. You can also get a cup of sand from a older system with good diversity. I know you don't have sand but you can add it to the sump or a bowel in the sump or display. There are millions of things that live in the sand.
Third: you need to get that fuge running at full capacity. Give the mangroves away, you are growing corals here not plants. Need the room for chaeto. Also if you have any sand or substrate I suggest removing it but that's your call. It would be better to have some small rocks in there as kind of pod hotels. Pods love refugiums because there is film algae to graze on and no fish to eat them. Providing them a place to live will help the population. Most important things are good flow and lighting in a chaeto refugium. You have a huge pump so try to get as much flow going through the fuge as you can. Second thing is you need a real grow light. I have this light and I harvest 5 gallons of chaeto every two weeks!
VIPARSPECTRA Reflector-Series 300W LED Grow Light Full Spectrum for Indoor Plants Veg and Flower
https://www.amazon.com/dp/B01B4GQ6MO/ref=cm_sw_r_cp_api_2EU2zbQ35ZEXH
The spectrum peaks exactly in the areas that are needed to support vigorous healthy growth from the chaeto. At 12" I think I measured about 1200 PAR so it will be plenty of light. The fuge size is perfect for the Kessil H380 and this light would be a home run. It's more costly but it will pay off.
I think that your system is young and when starting with dry rock that's basically sterile it takes a long time for everything to mature. Blooms will come and go as it does so don't have any knee jerk reactions. Best thing you can do is nothing at first but evaluate, test the water, check equipment, look at your habits and then research a fix of needed.
Water changes, do them. I built a water change station that collects my RODI and mixes the salt water. Only need to turn some valves and pump the water directly to my sump. Since then I've been changing ~100g every 1-2 weeks and my system hasn't ever been so healthy. I change a lot of water and that works for me. How ever you do them ensure it's at least 30% a month. More however is better.
To grow sticks you need high input/high output, stable clean water, and good light and flow. The algae problem will go away on its own if you continue to maintain good water. Manually clean off what you can, keeps DOCs low buy wet skimming, using and changing filters socks no more than every 3 days, run some GAC, and feed high quality foods. You may need GFO but if you get the fuge running well like mine and the PO4 will drop on its own.
I have to add Nitrates and occasionally Phosphorus to keep my corals happy. Both are required to support them. NO3 like to keep between 2-8ppm for best colors and growth. PO4 I keep low, I can no longer detect PO4 with my Hanna ULR Checker but I feed lots of foods so Phosphate is added daily just doesn't build up. It's being consumed at the same rate it's added. If my corals begins to pale and NO3 is ok then I'll know I need to add some Seachem Florish Phosphorus.
Your doing well and on the right track. The system is young and theses algae blooms happen. Just keep on keeping on.