If I open a new chat, and don't start typing anything in the input textbox, and click away, the chat should be automatically deleted and removed from the left-side chat history.

As-is, I sometimes will start a new chat, click off of it to go review another chat for context, then just click the new top "new chat" button again, leaving an empty "New Chat" in my history for no reason that goes unused, and just takes up space unless I manually go and delete it.

If I start typing something in the input box, its fine you can keep it to leave that context of what I was typing there. But if the input box is empty, I don't think there's any reason not to just delete it.