BillytheLid It depends what you consider a privacy nightmare. I believe you need ChatGPT plus to have private chat for example, or opt-out of training. I don't know if they fixed this but AFAIK if your profile was created with your microsoft account you can only use this account to log-in. You could also use the API access and experiment with cost and capabilities with https://platform.openai.com/playground/ Using their cheapest model e.g. 4o-mini is surprisingly dirt-cheap.
Perplexity is also an option and they have many options in term of pricing (e.g. pro subscription vs. paid api access). And nothing wrong if you prefer Claude or gemini. If you value your privacy then look at their API access and term of services, just like ChatGPT or any other provider.
Or you could run your own model locally. Ollama is quite popular, and so is openwebui. Personally running ollama from the cli is sufficent for my needs. I would recommend that you run that in a VM. You can absolutely run with cpu alone but if it's a laptop you might wan to make sure it's well ventilated because the ram will get hot. Even those stick-on copper/graphene heatsink improve heat transfer quite significantly, and disabling turbo boost and downclocking by 5-10% may help a lot.
I have not expiremented with running my own AI on my pixel.