Migrate publish.yml to 1ES PT (#12302)

## Description

This PR migrates our publish.yml on top of the required 1ES Pipeline Template, including some minor refactors to some template files to prevent them from conflicting with how the 1ES templates work.

### Type of Change
- New feature (non-breaking change which adds functionality)

### Why
Compliance push.

### What
Refactors the pipeline to be passed to the template, and added parameters to our templates that publish build artifacts to allow the publish to op-out, and let the 1ES template do that publish.

## Screenshots

![image](https://github.com/microsoft/react-native-windows/assets/10852185/a5986d42-388f-429c-b8d5-7cc0c1135785)

## Testing
Verified that the pipeline runs successfully.

## Changelog
Should this change be included in the release notes: yes

Converted publish.yml ADO pipeline to extend the v1/1ES.Official.PipelineTemplate.yml template