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Follow all mixing and application directions on the package.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

It is likely not you that did anything wrong. Sometimes the bud and bloom rosebushes in the pots are somewhat rootbound and never really come out of that and just die. Some roses are sold in those plastic bags at various stores. I call them Body Bag roses as the root systems have typically been cut back badly. While in the bag and wet they do fine and look quite healthy. But take them out of the bag and plant them in the ground and the entire situation changes big time! The root systems are so badly cut back that they cannot begin to support all the upper growth. So they die. I try one once in a while as a challenge to see if I can keep it going. My success rate has been about 25% and that is with a lot of babying. I also water all my rosebushes in with water that has both a product called Super Thrive and a root stimulator in it. Water with the same type mix the next 5 to 6 times they need watering. It helps them overcome any transplant shock and get the root system growing well. Happy root system spells happy top side!

Remove the worst affected leaves since they are no longer performing photosynthesis and contribute to other leaves becoming infected. Neem oil is one organic treatment. Other home recipes have uneven results. It is important to spray home remedies on a small portion of the plant and wait several days to see if the spray damaged the plant. Several home-made recipes follow: I can not vouch for their effectiveness or safety.
Blackspot and mildew control and prevention: Milk spray. Mix one part milk to 9 parts water. Spray every 5-7 days X 3 applications.
Powdery mildew formula: to one gallon water, add 4 tsp baking soda and 1 Tbl horticultural oil. Spray all leaf surfaces every 3 days X 3
Powdery mildew recipe: to one gallon of water, add
1 Tbl baking soda
2 Tbl Safer SunSpray (fine agricultural oil)
with or without anti-transpirant. Anti-transpirant keeps fungal spores from spreading.

Your rose should push forth new leaves. If you have them on a normal fertilizer schedule, add an extra dose of liquid fertilizer now. Pre-treat the new leaves to prevent black spot. Remove all plant debris from under the shrubs including mulch. Put down new mulch, 1-2 inches but not near the plant base. Consider removing the lowest most leaves. Splash from watering and rain can re-infect the shrub. Removing the lower leaves also improves air circulation which is important for a healthy rose. Remember when spring pruning to remove canes that grow toward the center; again, the point is to open up the bush to sunlight and air circulation.

I did not write the article. You are correct in pointing out this may be garden tradition than science. Here is an article from a soil scientist on magnesium in garden soil, the claims vs. the science. https://s3.wp.wsu.edu/uploads/sites/403/2015/03/epsom-salts.pdf