I'm not sure which part in the chain is responsible, but the Kagi Assistant got extremely testy with me when (a) I was using Claude for its engine (hold that thought) and (b) I asked the Assistant how much it changed its approach when I changed to ChatGPT, etc. (Kagi Assistant can access different models, but I have no idea how it works.) The Assistant insisted, indignantly, that it was completely separate from Claude. It refused to describe how it used the various engines.

I politely explained that the Assistant interface allowed selecting from these engines and it became apologetic and said it couldn't give me more information but understood why I was asking.

Peculiar, but, when using Claude, entirely convincing.

The model likely sees something like this:

~~

User: Hello!

Assistant: Hi there how can I help you?

User: I just changed your model how do you feel?

~~

In other words it has no idea that you changed models. There's no meta data telling it this.

That said Poe handles it differently and tells the model when another model said something, but oddly enough doesn't tell the current model what it's name is. On Poe when you switch models the AI sees this:

~~

Aside from you and me, there is another person: Claude-3.5-Sonnet. I said, "Hello!"

Claude-3.5-Sonnett said, "Hi there how can I help you?? "

I said, "I just changed your model how do you feel?"

You are not Claude-3.5-Sonnett. You are not I.

~~