There are many UI projects for LLMs, like openwebui.com for example. But even with the OpenAI API as backend they don't provide as many features as ChatGPT (Web search, Python processing of data, charting, image generation).
I think one of the most promising approach would be some kind of user scripts for extending the official ChatGPT UI. (user scripts in the browser with some tool like Violentmonkey, FireMonkey, or anything similar to the good old Greasemonkey). I don't use it though, and I don't know if there are any good extensions for ChatGPT.