Migrate Rust emitter to typespec-azure

## Summary

This issue tracks migrating the Rust emitter package from
[Azure/typespec-rust](https://github.com/Azure/typespec-rust)
to this repository (`Azure/typespec-azure`) to consolidate all Azure TypeSpec
emitters in one place.

## Motivation

- Consolidate all Azure language emitters alongside the shared Azure TypeSpec
libraries (`@azure-tools/typespec-azure-core`,
`@azure-tools/typespec-azure-resource-manager`,
`@azure-tools/typespec-client-generator-core`, etc.)
- Simplify cross-package development and testing
- Unified CI/CD, versioning, and release process
- Easier coordination between the Rust emitter and the shared Azure TypeSpec
libraries it depends on

## Current Location

- Repository: [Azure/typespec-rust](https://github.com/Azure/typespec-rust)

## Proposed Target Location

- Repository: `Azure/typespec-azure`

## Tasks

- [ ] Move the Rust emitter source from `Azure/typespec-rust`
- [ ] Update internal cross-package references
- [ ] Update CI/CD pipelines
- [ ] Update package references and documentation
- [ ] Archive or redirect the original location
- [ ] Verify all tests pass in the new location

Begin by comparing the Rust emitter source in Azure/typespec-rust with the target Azure/typespec-azure repository and inventorying its package references and CI/CD pipelines. Review the migration tasks and existing tests before changing anything. Done means the emitter is moved, references, pipelines, documentation, and the original repository location are handled, and all tests pass.

Written by the indexing model from the issue text.