>My best guess is -- ChatGPT is running something in your browser to try to determine the best things to send down to the model API
There's no way this is worth it unless the models are absolutely tiny, in which case any benefits from offloading to the client is marginal and probably isn't worth the engineering effort.
It’s free as a loss leader. The trick is to upsell later. Unfortunately for OpenAI there are plenty of competitors with fungible products, so it might be hard to pull a classic monopoly rug-pull.