I'm a beginner gardener, and I've been growing some basil cuttings for a little over 2 months. It was going well for a while, but recently I've noticed some troubling things happening to them. For starters, they started to grow faint spots on their foliage. It's not visible from afar, but very clear when you get up close. I thought that it was powdery mildew, so I sprayed a bit of neem oil on the leaves during the early morning (to avoid the leaves burning). It showed signs of improvement for a day or two, but now some of the leaves have started to wilt and dry, and the spots have shown no signs of improvement.
Also, one of my basil plants seems to be drooping, and can't grow straight. Usually I'd chalk it up to me accidentally letting it lean a bit too much towards the sun, but the leaves also don't seem as robust and are slightly more droopy than the other plants, so I'm assuming it's unwell (this occurred a few weeks before the spots). What should I do?

yang06dog
So far your basil have done pretty well, but here in the northern hemisphere we're in the shortest, coolest days; not the best conditions for this hot weather crop.

I can't tell for certain from the photos and you don't give your location, but here's my first thought: most likely environmental and yes, probably mildew or a fungal infection. They need more sunlight and more heat, good drainage and good air circulation. A lot more of each, which can be difficult indoors. Remove every leaf with sunken patches or that appears unhealthy and correct the growing conditions. Good luck!

Thank you for the tips! I'll follow them to the best of my abilities. I purchased a fungicide earlier this week and I'll start applying it onto the leaves. I'm also going to buy a mini fan to improve air circulation. As for the drainage, I don't think I have the time to properly repot them and add drainage material, but I'll probably water them more infrequently to reduce the risk of them getting waterlogged.
I'll update if the basil gets better. Thanks!

Basil has long roots that do not like to get their feet wet, deeper soil/drainage is good, keep away from cold spots and need lower air humidity, however, down here near Houston, I am having almost zero luck this year with my cuttings sprouting. Do not use potting soil on basils, it holds too much moisture for the plant. Basils - like most aromatics - were basically weeds that we liked the smell of - they grow best with neglect (a little, anyway) Good luck!