fix(trace-viewer): Copy request body when copying network request

[cpAdm]

Sidenote: The original code from chrome devtools has since been updated

Closes: #38590

[yury-s]

Sidenote: The original code from chrome devtools has since been updated

Feel free to roll it to Playwright.

[github-actions]

Test results for "MCP"

1 failed
❌ [chrome] › mcp/test-setup.spec.ts:81 › test_run should run global setup and teardown @mcp-macos-15

2726 passed, 116 skipped

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Merge workflow run.

[github-actions]

Test results for "tests 1"

1 failed
❌ [playwright-test] › playwright.spec.ts:877 › page.pause() should disable test timeout @macos-latest-node20-1

3 flaky

⚠️ [chromium-library] › library/trace-viewer.spec.ts:1420 › should highlight locator in iframe while typing `@chromium-ubuntu-22.04-node20`
⚠️ [firefox-library] › library/inspector/cli-codegen-1.spec.ts:1082 › cli codegen › should not throw csp directive violation errors `@firefox-ubuntu-22.04-node20`
⚠️ [playwright-test] › runner.spec.ts:124 › should ignore subprocess creation error because of SIGINT `@macos-latest-node20-2`

34394 passed, 689 skipped

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Merge workflow run.