fix(screencast): deliver cached last frame to additional clients

[dgozman]

Summary

• Cache the last screencast frame on the server and, when another client joins an already-active screencast, deliver it on the next tick.
• Drop the dashboard's page.screenshot() workaround that forced a first frame.

Fixes #40349

[github-actions]

Test results for "tests 1"

11 flaky

⚠️ [chromium-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@ubuntu-22.04-chromium-tip-of-tree`
⚠️ [chromium-library] › library/video.spec.ts:719 › screencast › should work with video+trace `@ubuntu-22.04-chromium-tip-of-tree`
⚠️ [chromium-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@chromium-ubuntu-22.04-arm-node20`
⚠️ [chromium-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@chromium-ubuntu-22.04-node24`
⚠️ [chromium-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@chromium-ubuntu-22.04-node20`
⚠️ [chromium-library] › library/video.spec.ts:476 › screencast › should capture static page in persistent context @smoke `@chromium-ubuntu-22.04-node20`
⚠️ [chromium-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@chromium-ubuntu-22.04-node22`
⚠️ [firefox-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@firefox-ubuntu-22.04-node20`
⚠️ [firefox-library] › library/inspector/cli-codegen-1.spec.ts:1080 › cli codegen › should not throw csp directive violation errors `@firefox-ubuntu-22.04-node20`
⚠️ [firefox-page] › page/page-wait-for-function.spec.ts:104 › should work with strict CSP policy `@firefox-ubuntu-22.04-node20`
⚠️ [webkit-library] › library/browser.spec.ts:73 › newContext should not leave a context upon failure `@webkit-ubuntu-22.04-node20`

41313 passed, 847 skipped

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Merge workflow run.

[github-actions]

Test results for "MCP"

7 failed
❌ [chrome] › mcp/dashboard.spec.ts:229 › should switch screencast to -s session on show --annotate @mcp-windows-latest
❌ [chromium] › mcp/dashboard.spec.ts:229 › should switch screencast to -s session on show --annotate @mcp-windows-latest
❌ [firefox] › mcp/cli-session.spec.ts:99 › delete-data @mcp-windows-latest
❌ [firefox] › mcp/cli-session.spec.ts:191 › list --all lists sessions from all workspaces @mcp-windows-latest
❌ [chrome] › mcp/dashboard.spec.ts:229 › should switch screencast to -s session on show --annotate @mcp-macos-latest
❌ [webkit] › mcp/dashboard.spec.ts:229 › should switch screencast to -s session on show --annotate @mcp-windows-latest
❌ [msedge] › mcp/dashboard.spec.ts:229 › should switch screencast to -s session on show --annotate @mcp-windows-latest

6578 passed, 916 skipped

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Merge workflow run.