Feathers needs better examples

There are multiple steps to this, each of which probably deserves its own PR for ease of review:

- [ ] Rename the existing example to `feathers_example_showcase`.
- [ ] Move all of the `feathers` examples into a subfolder under UI examples.
- [ ] Create a new, minimal getting-started-with-feathers example.
- [ ] Create a new very short example for each feathers widget.

Start by locating the existing Feathers examples and the UI examples directory, then review how the current examples are organized. The work is complete when the existing example is renamed, Feathers examples are grouped, a minimal getting-started example exists, and each Feathers widget has a short example.

Written by the indexing model from the issue text.