[Feature] a dedicated clipboard API

It might be nice to have a dedicated clipboard API scoped to page.

Some ideas:

```js
await page.pasteText(text);
await page.keyboard.press('Ctrl + V');
await page.copySelection();
await context.clipboard.setContent(mimeType, content);
```

No implementation files, tests, or entry points are named. Start by clarifying which clipboard operations and scopes are required from the proposed page, keyboard, and context APIs, then identify the relevant Playwright API and test areas. Done would require an agreed API design, implementation scope, and tests for the supported clipboard behavior.

Written by the indexing model from the issue text.