It's somewhat ambiguous language - "self-hosted ChatGPT UI" could lead many to believe it's completely self-hosted.

However, sophisticated readers familiar with ChatGPT will know the model and weights haven't been released and absent a leak/hack/release by OpenAI a completely self-hosted ChatGPT solution is impossible. Eventually we'll almost certainly see a "Completely self-hosted ChatGPT equivalent" (similar to Dall-E vs Stable Diffusion) but that's another thread for another time.

Based on my native speaker parsing of English "Self-hosted ChatGPT UI" is accurate and I'm not sure how else I would write it to disambiguate between a self-hosted UI and a completely self-hosted ChatGPT with a UI.