How do bypasses work in general?

Hey, I'm curious about bypasses, for those who have good experience on the topic. I apologize if this has been asked many times. I have a fair amount of experience hacking and I know C++/C/Assembly and understand memory and pointers well enough. I genuinely have no idea how a bypass works, though, and I imagine bypassing something like BattlEye would be difficult as hell, especially since I've never actually seen a hacker in Fortnite. I also hear Blizzard games like Overwatch are incredibly difficult to hack due to anti-cheat.

The only sort of security bypass I've attempted is bypassing the anti-debugger in CSS (and it didn't even work well). Basically the game would change the function that would be called when the debugger was attached so that it would exit the program instead. The fix for this was to patch this array of bytes that exit the program to bring it back to normal.

This is the only experience I've had with bypassing any sort of security in software. I understand "How do bypasses work?" is a very broad and vague question. I'm going to assume that different anti-cheats might have very different methods of protecting the game. Basically, I'm wondering how bypasses work at a basic level. Do all anti-cheats share some sort of similarities that all bypasses work around to an extent? What's an example of an anti-cheat and how it works and how it's bypassed?

Thanks.

I see that noone else has responded. There are several different ways to get around anticheats;
1. You could invent a new method of achieving the same effect, due to it not being known to the anticheats yet it is likely to be undetected.
2. You could inject code into the anticheat, and force it to return clean scans(this is going to be fairly difficult)
3. You could code an external cheat and only read from memory, this usually lowers your detection chances as well.