Remove workspace from root of repo

Initially, we wanted to bundle the web application into the distributed binary via `embeddable-web-client`. The plan has changed since Docker is now the recommended method for hosting a competition.

Because of this, we no longer need the workspace or the `embeddable-web-client` binary, so they can be removed. The application itself can also be moved out of the `client` directory into the root.

- [ ] Remove `embeddable-web-client`
- [ ] Remove cargo workspace
- [ ] Move application out of `client`

Inspect the repository root, the client directory, the Cargo workspace configuration, and the embeddable-web-client target first. Done means the binary and workspace are removed and the application has been moved from client into the repository root, as described by the checklist.

Written by the indexing model from the issue text.