dist rename rollout plan

In #1267, we're working towards renaming `cargo-dist` to `dist`. We have a few steps to do in this release and in the releases to follow.

## Now

- [x] Replace all user-facing references to `cargo-dist` with `dist`, except in the names of the installers and related packages
- [x] Thoroughly test the new `dist` binary and its `cargo-dist` alias, ensuring it works both ways
- [x] Update the documentation with the new name
- [x] Write a blog post announcing the new name

## When 0.24.0 is released

- [x] Publish doc changes
- [x] Publish blog post

## After 0.24.0 is released

- [ ] Prepare to rename the package so that future installers use the name `dist` instead of `cargo-dist`
- [ ] Ensure the Homebrew package can retain its name for compatibility OR use a Homebrew tap rename to handle the Homebrew name change
- [ ] Decide how to handle crates.io package name changes
- [ ] Cut a minor release with these changes

## Sometime after that minor release

- [ ] Cut a release under the new package name, so the intermediate release has a package to upgrade to

Start by reviewing the rename work in #1267 and the current release, installer, Homebrew, and crates.io packaging configuration. Map the remaining package-name and upgrade-path decisions before making changes. Done means the post-0.24.0 rename plan is implemented, compatibility is preserved, and the listed follow-up releases can be cut.

Written by the indexing model from the issue text.