[Epic][TypeSpec Authoring] Support writing examples in authoring stage

## Overview

This epic tracks work to support writing examples during the TypeSpec authoring stage. The goal is to enable authors to create, validate, and manage API examples (operation request/response samples) as part of authoring their TypeSpec, so examples are correct and available early rather than added later in the pipeline.

## Problem

Today examples are typically authored or generated late in the process, disconnected from the authoring experience. Authors lack first-class support for writing examples alongside their TypeSpec, validating them against the models/operations they describe, and catching mismatches early. This leads to missing, incomplete, or invalid examples surfacing downstream.

## Sub-Issues

- Tracked below as sub-issues.