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Even the first entry is wrong, the firmware is not open source.
Projects whose source code has leaked generally aren't.
That said my cursory Google search turned up nothing relating to the source code of the firmware so
IIRC the PS3 had it's firmware encryption key published not the source code.
Correct. And the private encryption key was derived because during encryption sony didnt use a random number at every encryption, but a constant instead. So a few math operations with the public key and tada, it you have the private key
And unless I'm missing something, this was in 2012, not 2011.
I think you phrased that wrong. I think you're claiming that the firmware was never leaked. ChatGPT did not claim the firmware was open source. It's a pretty easy brainfart to make and say "open" when you mean "(now) public".