Yup, want privacy, host your own models. Perplexica Vane + ollama (or Lemonade, better for AMD) is pretty damn easy to stand up and works well I find (never used perplexity) and you get references to real web pages to double check for hallucinations.

Nice thing about deep research is you can ask a question and just come back later, so latency is less of an issue, even CPU + RAM can do the job.

Given the current state of the internet it's heading towards a necessity to play Spy vs Spy AI Slop vs AI Slop. Might as well control it yourself.

FWIW I find Qwen 3.5 27B a great model if you can fit it (and I use the perplexity embedding model that they open weighted pplx-embed).