Add --quiet support to pr checks --watch and run watch

### Describe the feature or problem you’d like to solve

I would first like to ask whether quiet watch output would be useful for coding agents.

When an agent waits for pull request checks or a workflow run to complete, it generally only needs the final result before deciding what to do next. Today, `gh pr checks --watch` and `gh run watch` continuously render intermediate status updates. These updates are useful for someone actively watching a terminal, but they can add unnecessary noise to an agent's context without providing an actionable result.

It may be helpful to let agents wait for completion while receiving only the final output, without changing the existing interactive behavior by default.

### Proposed solution

Add a `--quiet` option to both watch flows:

- `gh pr checks --watch --quiet`
- `gh run watch --quiet`

When enabled, the option would:

- Suppress intermediate refresh messages and status renders.
- Avoid alternate-screen progress updates.
- Print the normal final summary or run result after completion.
- Preserve the existing exit status behavior.

Without `--quiet`, both commands would continue to behave exactly as they do today.

### Additional context

The main question is whether these options would meaningfully improve agent workflows by avoiding unnecessary intermediate output. If another existing output mode or a different design would better address this use case, I would be happy to consider that instead.

If this seems useful, I happen to have a [PR](https://github.com/cli/cli/pull/13993) ready with the proposed implementation and tests. If it does not seem useful, please feel free to close both the issue and the [PR](https://github.com/cli/cli/pull/13993).

Start by reviewing the existing `gh pr checks --watch` and `gh run watch` entry points, then inspect PR #13993 and its tests for the proposed behavior. Done means both commands accept `--quiet`, suppress intermediate and alternate-screen updates, print the normal final result, and preserve existing exit statuses.

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