This is an anthropomorphization. LLMs do not think they are anything, no concept of self, no thinking at all (despite the lovely marketing around thinking/reasoning models). I'm quite sad that more hasn't been done to dispel this.
When you ask gpt 4.1 et c to describe itself, it doesn't have singular concept of "itself". It has some training data around what LLMs are in general and can feed back a reasonable response given.