I figured out what the problem is, and also how the caliper works.
The problem is, even though there's plenty of pad left on the shoes or whatever there called, there's not enough for the caliper to work. What was actually happening when it felt like the cable was slipping through the screw, was the caliper was reaching the end of its travel before the pads grabbed the disc. Just to be scientific, I removed the piece of metal that I put between a pad and the magnet that holds it. After I did that, the caliper behaved the way it before I started trying fix it. I figured out the pads were the problem because I know I had everything adjusted properly, so that's all it could be. I also looked at pictures of new brake shoes or whatever their called and the pad on them is about twice as thick as what my pads have left.
You use probably at least 90% of the pad on disc brakes on a car before you hear a scraping noise(caused by a metal thing mounted on the caliper or the shoe that scrapes the disc when the pad is used up enough). Why don't bicycle disc brakes work that way? Because there's so much pad left on the shoes, I didn't consider that to be the problem back when I started trying to fix the problem.
I also figured how the caliper works. The pad on the opposite side of where the arm is, is pushed by that entire side of the caliper being pulled towards the disc. That's why there's 2 springs inside the mechanism. I think the pads being worn too low made it see like the mechanism wasn't working properly. I'm just gonna put the piece of metal back between the shoe and the magnet to use as much pad as I can before getting new ones. I put it between the shoe and the magnet on the other side this time to see if it worked any differently on that side, and it doesn't.
I wanted to thank you guys for helping me, but I think I've been mostly helping myself and entertaining you.😂 But I'll thank you anyway.