I can't speak to the coral as I never kept that in my fresh water aquariums. It sounds like you had an established tank so the most likely culprit is the recently added fish, the neon tetras. Did your fish exhibit any signs of illness prior the mass die off? You mention a list of fairly hardy to extremely hardy fish so without obvious signs of illness I don't quite know else besides illness to suggest. Do you know if your heater went crazy? I had that happen once and all of my fish were overheated and died. At any rate it would seem something went drastically wrong with your established tank and illness would be my first thought. If you have a reputable fish dealer, go there for their advice. Depending on what they say it would drive how far I would clean my tank and what steps to take next.
I will caution you that a planted tank is work. You have to ensure you add enough CO2 to the tank to sustain the plants. Plus you need the correct light spectrum for sufficient hours per day and you need substrate intended for planted aquariums. Purchasing healthy plants was tough in my area and more often than not they came home infested with snails which is a whole other world of problems. I presume you have researched all that but mention it nonetheless.
Personally if I believed illness were to blame, I would make one decision right now - planted tank or fish only tank. Once I decided which route I want to go, I would start by cleaning everything (stripping the filter all the way down, washing it and adding back fresh, recommended filter media) and then cycling the tank from scratch before adding any fish. It's the long route but the one I had the most success with; there are lots of good sources for cycling a tank to get it up and running. For a planted tank this fresh start approach would mean adding plant substrate as the base layer, adding CO2 to the tank, installing the appropriate light fixture, adding the plants and then cycling the tank. If it were a fish only tank, then it would mean adding gravel and then cycling the tank. Once the tank had cycled sufficiently (six weeks approximately), then I would begin adding small batches of inexpensive fish, tetras and danios for instance.
It’s been a few years since we kept an aquarium but there are tons of good websites out there. We had better luck with larger tanks than we did small. The chemical levels don’t swing as much and the temperature is easier to keep stable. We also found shortcuts only lead to fish death so I would urge you to take the slow and steady route. Whatever you do, good luck and may you not have another mass extinction.