feat: integrate with Noice + use as cmdline UI?

I was wondering if there is a way to completely replace/override all of neovim's messages, or is that a separate functionality that needs to be developed? And I mean not just the notifications, but things that are in the cmdline like prints, when you save a file, etc. Every message.
The idea is to have `cmdheight = 0`

[Noice](https://github.com/folke/noice.nvim) does this with it's notifications, but I think fidged looks better than the 2 notification backends provided by noice. Maybe fidget can colab and also be included as a backend?

The issue names no files or tests; start by reviewing Fidget's existing notification handling and how Neovim surfaces cmdline messages. Compare the requested scope with Noice's notification backend model. Done means the integration scope is decided for notifications, prints, save messages, and cmdheight=0 behavior.

Written by the indexing model from the issue text.