The processing that happens during a plugin’s operation just has whatever text the programmers thought was good feedback to make the user understand there will be a delay in the answer and to be patient. “sending your personal information across the internet to an undisclosed developer’s API” may be more accurate, but “thinking” works.
And the AI might not be able to think about things internally before it starts generating tokens, but it can be put into a convincing state, where an apology doesn’t anger you in context.