Based on history, I don't think changing from a permissive OSS license will allow it to remain the most popular, most full-y featured project, especially in a world of competitors (plenty of which have venture funding).
MSTY is the first one that comes to mind though. And if you're willing to stretch your idea of "what competes with OpenWebUI" I know half a dozen startups that let you pass in some set of keys and "build a multi-agent system" in a GUI usually alongside some pared down chat windows.
Could you give names of those startups?
And yeah, Hugging Face is very much venture funded -- they had a modest 4.5b valuation in the last round.. (I just didn't know they had some competing product).