Render [!NOTE] and [!WARNING] blocks in crate documentation

[azaleacolburn]

When the readme gets rendered in crates.io, [!NOTE] and [!WARNING] blocks don't get rendered as they would in GitHub (see below). In my opinion, it would be best to render these blocks so maintainers don't have to maintain separate readmes for GitHub and crates.io, or remove the blocks entirely. In other words, we should fully adopt GitHub's markdown standard.

Note

Foo

[LawnGnome]

This is a duplicate of #8506, which has had some work done in #10429, but unfortunately still needs some love before being ready to merge.