This change is for an internal IDE client to send a custom hot reload
request, as custom requests from the client must start with `$/`.

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above. (this PR is linked internally)
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/wiki/Tree-hygiene#overview
[Tree Hygiene]: https://github.com/flutter/flutter/wiki/Tree-hygiene
[test-exempt]:
https://github.com/flutter/flutter/wiki/Tree-hygiene#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo#features-we-expect-every-widget-to-implement
[CLA]: https://cla.developers.google.com/
[flutter/tests]: https://github.com/flutter/tests
[breaking change policy]:
https://github.com/flutter/flutter/wiki/Tree-hygiene#handling-breaking-changes
[Discord]: https://github.com/flutter/flutter/wiki/Chat