>Maybe I am underestimating
You sure are. And it sounds like you are also underestimating the effect yourself as well. In fact this perception is so common that there is even a name for it in psychology: Third-person effect. Many people believe that advertising does not affect them. But ironically, the more you believe so, the more likely you are to fall victim to particular types of advertising. And in general your response to ads will be very similar to everyone else's. These "annoying" ads that you "would never click on" are just badly personalized or badly placed ads. That's the only type that gets stuck in your mind when you think of ads, based on your personal biases. But the major tech companies have spent the last one-and-a-half decades on perfecting the psychology of advertising. You might think you are immune, but you are certainly not. Every buying decision you have made in the last 10 years was almost certainly influenced to some degree. Just not always consciously. And I'm willing to bet that a lot of buying decisions were already heavily influenced by ChatGPT, even before their shopping feature. OpenAI just didn't profit on them as much as they could.
Influenced to some degree sure, weather influences me to some degree, but I truly feel like ads aren't affective on me. Unless we broaden definition of ads to something like sponsored content. I have bought some TTRPG rules sets after I have seen them being played in a sponsored video, but I still have never clicked an ad on a page and bought something.
And I actually have tried to use ChatGPT to buy something. I have asked it to search for specific items from EU stores so I wouldn't need to pay import taxes, but usually it fails. It either suggests Global stores which ship from US or China or it suggests different products than what I asked for.
If ChatGPT or whatever LLM I was using could actually link me the products I wanted without me searching for them they should get a commission for sure, but we sure aren't there yet.