Migrate from `react-native-windows-init` to `react-native init-windows` for new RNW projects

[jonthysell]

This item tracks all the work necessary to build a new simpler path for creating new RNW projects, with a primary focus of enabling the React Native New Architecture and golden-path supported scenarios.

Tasks

#### Create named "old architecture" templates from existing UWP templates (in `/vnext`)
- [ ] https://github.com/microsoft/react-native-windows/issues/12147
- [ ] https://github.com/microsoft/react-native-windows/issues/12148
- [ ] https://github.com/microsoft/react-native-windows/issues/12149
- [ ] https://github.com/microsoft/react-native-windows/issues/12150

#### Create named "new architecture" templates (in `/vnext`)
- [ ] #11908
- [ ] https://github.com/microsoft/react-native-windows/issues/12171
- [ ] https://github.com/microsoft/react-native-windows/issues/12480

#### Create RNW CLI `init-windows` command  (in `/packages/@react-native-windows/cli`)
- [ ] https://github.com/microsoft/react-native-windows/issues/12151
- [ ] https://github.com/microsoft/react-native-windows/issues/12152
- [ ] Add functionality for `init-windows` to list available templates (with descriptions?)
- [ ] Add functionality for `init-windows` to specify callbacks to be called with a given template, and some common utilities (like modifying package.json or jest/metro configuration files, rather than stamping over them)
- [ ] Expose `initWindowsInternal()` such that other scripts could call it directly

#### Stop using `react-native-windows-init`
- [ ] Put checks in `react-native-windows-init` to prevent trying to target newer RN / RNW versions and give useful error messages to the user
- [ ] Delete the `jobs/cli-init.yml` jobs still calling `react-native-windows-init`

#### Documentation / Samples
- [ ] https://github.com/microsoft/react-native-windows/issues/13394
- [ ] Update samples upgrade steps / CI to use the new `react-native init-windows`
- [ ] Remove references to deprecated CLI arguments (refer to using `ExperimentalFeatures.props` where appropriate)
- [ ] Add upgrade documentation for users attempting to transition old apps to the new templates using `react-native init-windows`

#### Deprecate and remove old code
- [ ] #11744
- [ ] After RNW Paper is no longer supported, delete the old template code from RNW
- [ ] After RNW Paper is no longer supported, delete the `react-native-windows-init` package all together

[jonthysell]

Background context:

RNW Init v1

RNW Init v1: Basics

• Customers start with a React Native app, typically having been created by the npx react-native init command
  • This includes the JS app code and native app hosts for iOS / Android
• To add Windows support via RNW, customers use the npx react-native-windows-init command
  • This adds our RNW dependencies and a native app host for Windows
• This new project functionality is primarily accomplished by these three RNW packages:
  1. react-native-windows-init
  2. react-native-windows
  3. @react-native-windows/cli

RNW Init v1: Package Versioning

RNW Init v1: CLI Arguments

Argument	Type	Default	Req.	Hidden	Description
--help	bool	False	N	N	Show Help
--version	string	Auto¹	Y¹	N	Specify RNW version
--namespace	string	Auto²	Y²	N	Specify namespace for native code
--language	string	"cpp"	Y	N	Specify programming language C++ or C#
--projectType	string	"app"	N	N	Specify app or library (0.64+)
--useWinUI3	bool	False	N	Y	Target WinUI 3.0 instead of UWP XAML
--useHermes	bool	False	N	Y	Use Hermes instead of Chakra (0.64+)
--experimentalNuGetDependency	bool	False	N	Y	Build against Microsoft.ReactNative NuGet instead of source
--verbose	bool	False	N	N	Verbose output
--overwrite	bool	False	N	N	Overwrite files without prompting
--telemetry	bool	False	N	N	Send usage telemetry to MSFT
--useDevMode	bool	False	N	Y	Use local RNW clone
--nuGetTestFeed	string	""	N	Y	Use specified NuGet test feed
--nuGetTestVersion	string	""	N	Y	Use specified NuGet test version

¹: If unspecified, calculated based on existing project RN version ²: If unspecified, calculated based on existing project name

RNW Init v1: Code Flow

[jonthysell]

More background context:

The Problems

1. The latest RNW Init must support all past versions of RNW
   1. The ABI between the packages is static
2. There are too many CLI arguments
   1. Produces a rather large matrix of combinations (not all supported)
   2. Not every argument is supported by every RNW version
   3. Experimental Features as args means we can’t deprecate args
3. Important changes to experimental features in the near/medium term
   1. Removing the WinUI3 template project
   2. Switch to Hermes as the default engine
   3. Switch to Fabric as the default architecture
   4. Switch to consuming NuGet instead of source
4. No way to invoke project init without RNW Init

[chrisglein]

@jonthysell FYI adding link to #13362. Resolve when appropriate.