[BUG] Clipboard API, ClipboardItem not working in headless (chromium)

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### System info
- Playwright Version: [v1.35.0]
- Operating System: [Windows 10, Linux 3.10.0-1160.25.1.el7.x86_64, Mac]
- Browser: [Chromium]
- Other info: [Copy pasting works but I can not copy or paste ClipboardItem, this works if I use the puppeteer browser or headed Playwright Chromium]

or

**Config file**

```js
// playwright.config.ts
import { PlaywrightTestConfig } from '@playwright/test';
import * as puppeteer from 'puppeteer';
const whiteListDomains = '*scania.com';
const chromiumFlags = [
'--auth-negotiate-delegate-whitelist='+whiteListDomains,
'--auth-schemes="basic,ntlm,negotiate"',
'--auth-server-allowlist='+whiteListDomains,
/**
* @deprecated will be removed in future chromium versions
*/
'--auth-server-whitelist='+whiteListDomains,
'--disable-dev-shm-usage',
'--disable-extensions',
'--disable-setuid-sandbox',
'--no-sandbox',
'--window-size=1920,1200'
];
/**
* See https://playwright.dev/docs/test-configuration.
*/
const config: PlaywrightTestConfig = {
//testMatch: /.*(e2e-spec)\.(js|ts|mjs)/,
testMatch: '**/*.e2e-spec.ts',
testIgnore: ['**/productcoord1.e2e-spec.ts**', '**/copy.paste.e2e-spec.ts'],
/* Maximum time one test can run for. */
timeout: process.env.CI ? 120 * 1000 : 60 * 1000,

globalSetup: './playwright.setup.ts',
expect: {
/**
* Maximum time expect() should wait for the condition to be met.
* For example in `await expect(locator).toHaveText();`
*/
timeout: process.env.CI ? 15 * 1000 : 10 * 1000
},
/* Run tests in files in parallel */
fullyParallel: true,
/* Fail the build on CI if you accidentally left test.only in the source code. */
forbidOnly: !!process.env.CI,
/* Retry on CI only */
retries: process.env.CI ? 2 : 0,
/* Opt out of parallel tests on CI. */
workers: process.env.CI ? 30 : 4,
/* Reporter to use. See https://playwright.dev/docs/test-reporters */

reporter: process.env.CI ? [
['list'],
['../internal-lib-e2e/src/reporters/rerun-reporter'],
['html', { outputFolder: '.test_results/'+ process.env.SUITE }],
['../internal-lib-e2e/src/reporters/rerun-reporter']
] : [
['list'],
['html', { outputFolder: '.test_results/test_report' }]
],
/* Shared settings for all the projects below. See https://playwright.dev/docs/api/class-testoptions. */
use: {
actionTimeout: 0,
trace: process.env.CI ? 'retain-on-failure' : 'on',
screenshot: process.env.CI ? 'only-on-failure' : 'on',
video: process.env.CI ? 'retain-on-failure' : 'on',
viewport: null
},
/* Configure projects for major browsers */
projects: [
{
name: 'full',
use: {
browserName: 'chromium',
permissions: ['clipboard-read', 'clipboard-write'],
contextOptions: {
permissions: ['clipboard-read', 'clipboard-write']
},
launchOptions: {
args: chromiumFlags,
executablePath: undefined
}
}
},
{
name: 'auth',
testMatch: '**/productcoord1.e2e-spec.ts',
testIgnore: '',
use: {
browserName: 'chromium',
permissions: ['clipboard-read', 'clipboard-write'],
contextOptions: {
permissions: ['clipboard-read', 'clipboard-write']
},
launchOptions: {
args: chromiumFlags,
executablePath: undefined
}
}
},
{
name: 'copy',
testMatch: '**/copy.paste.e2e-spec.ts',
testIgnore: '',
use: {
browserName: 'chromium',
permissions: ['clipboard-read', 'clipboard-write'],
contextOptions: {
permissions: ['clipboard-read', 'clipboard-write']
},
launchOptions: {
args: chromiumFlags,
executablePath: process.env.CI ? puppeteer.executablePath() : undefined
}
}
}
],
outputDir: '.test_results/output'
};

export default config;

```

**Steps**
- [Run the test]
- [The test copies the raw text instead of giving me the ClipboardItem]

**Expected**

[I expect to have the ClipboardItem in my clipboard instead of the raw text]

**Actual**

[I get the raw text]

This works in headed Playwright Chromium and headless puppeteer Chromium 107

Start with the inline playwright.config.ts configuration and the excluded copy.paste.e2e-spec.ts test, then reproduce the ClipboardItem behavior in headless and headed Chromium using the listed permissions and launch options. Compare the resulting clipboard contents; done means headless Chromium preserves the ClipboardItem rather than returning only raw text.

Written by the indexing model from the issue text.