chore: follow up to video api changes

[dgozman]

• Fix a bug in FFPage initialization.
• Bring back saveAs({ path }).
• Do not check for isStorageStatePage in screencast.

See #39054 for reference.

[github-actions]

Test results for "tests 1"

2 failed
❌ [playwright-test] › reporter.spec.ts:251 › created › should not have internal error when steps are finished after timeout @macos-latest-node20
❌ [playwright-test] › ui-mode-test-network-tab.spec.ts:301 › should copy network request @macos-latest-node20

2 flaky

⚠️ [firefox-page] › page/page-wait-for-function.spec.ts:104 › should work with strict CSP policy `@firefox-ubuntu-22.04-node20`
⚠️ [webkit-page] › page/page-autowaiting-basic.spec.ts:79 › should await form-post on click `@webkit-ubuntu-22.04-node20`

34261 passed, 662 skipped

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Merge workflow run.

[github-actions]

Test results for "MCP"

16 failed
❌ [chrome] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-ubuntu-latest
❌ [chromium] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-ubuntu-latest
❌ [firefox] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-ubuntu-latest
❌ [webkit] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-ubuntu-latest
❌ [chrome] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-windows-latest
❌ [chromium] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-windows-latest
❌ [firefox] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-windows-latest
❌ [webkit] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-windows-latest
❌ [msedge] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-windows-latest
❌ [chrome] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-macos-15
❌ [chrome] › mcp/cli-misc.spec.ts:28 › old client @mcp-macos-15
❌ [chrome] › mcp/cli-save-as.spec.ts:35 › screenshot --full-page @mcp-macos-15
❌ [chromium] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-macos-15
❌ [chromium] › mcp/launch.spec.ts:21 › test reopen browser @mcp-macos-15
❌ [firefox] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-macos-15
❌ [webkit] › mcp/capabilities.spec.ts:19 › test snapshot tool list @mcp-macos-15

4478 passed, 147 skipped

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Merge workflow run.