but the odds that I and others even reached one with an already used balance proves that private key collision is a common occurrence even given the trillions to 1 odds.
There's only one way to prove a private key collision: show 2 different private keys that both produce the same address. Nobody has been able to do that yet.
You can't brute-forcing a random private key. The only way to find it, is if it's not really random (or if someone leaks it).
That's not what a collision is, a collision is two separate generators generating the same private key that points to the same address. Not two different keys pointing to the same address. The private key is the root of an address. The address is simply the hash of that private key.