I suppose when it comes to depicting Koishi, the question would be how lucid we think she is. What does it mean for her to not think anything, running on instincts?
We can argue that something like googling herself might be deliberate enough to require relatively complex thoughts. But then it really is just putting your own name in the search bar, and the initial thought is almost as simple as instinct – what will Google give me if I put my name in?