"I paid money to someone to write that code" is exactly the line of argument that would lead to no copyright. There was the famous monkey selfie court case in 2015 that ruled that at least in the US, monkeys can't hold copyright. The same arguments would apply to AI. And since the AI can't create copyrighted works on its own, it can't assign copyright for works it created for hire either

The other line of argument is the "Claude Code is to coding like a photo camera is to painting". The image is generated automatically, but the input in how you point the camera is enough to still make it a creative work protected by copyright. Under that interpretation, you are not hiring AI, you are using it like a tool

The US Copyright Office holds the former opinion. I'm sure once this goes to court, lots of companies will vehemently argue the latter. I would not be surprised if we even end up changing the law over this