Autolinking should use the correct template as source files for autolinking codegen

[jonthysell]

Problem Description

Right now, autolinking always uses the template files from the old templates to generate the right includes. This precludes us from differentiating what those files look like in fabric.

Autolinking should load the correct template files for fabric instead of using the paper ones.

Steps To Reproduce

Run autolinking on fabric app project

Expected Results

No response

CLI version

npx @react-native-community/cli -v

Environment

npx @react-native-community/cli info

Community Modules

No response

Target Platform Version

None

Target Device(s)

No response

Visual Studio Version

None

Build Configuration

None

Snack, code example, screenshot, or link to a repository

No response