fix(mcp): preserve directory for additional tab videos

[yury-s]

Summary

• browser_start_video dropped the directory part of the filename for videos recorded from additional tabs (recordings/video.webm → video-1.webm) because the numeric suffix was applied with path.basename.
• Preserve path.dirname so additional tab videos land next to the first (recordings/video-1.webm).

Fixes #41659

[Skn0tt]

Trying out a CI failure triage bot we're building - here's its verdict on this PR's failing checks, posting by hand for now so we can see it in context:

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Hi, I'm the Playwright bot and I took a look at the failing CI.

🔴 video-start-stop fails on Windows because of this change

The 5 mcp/cli-devtools.spec.ts:217 › video-start-stop failures (all on @mcp-windows-latest-*) are caused by this PR. path.join() uses the OS separator, so on Windows the second video path comes out as recordings\video-1.webm, but the test asserts the forward-slash recordings/video-1.webm. This test passed on all 115 prior runs in the CI results DB — the only thing that changed is this PR. The other two failures are pre-existing flakes on unrelated PRs.

Details

Caused by this PR

• [chrome|chromium|firefox|msedge|webkit] › mcp/cli-devtools.spec.ts:217 › video-start-stop (5×, all @mcp-windows-latest-*) — the switch to path.join(dir, path.basename(...) + suffix + ext) in backend/context.ts produces a \ separator on Windows, so the suffixed video is emitted as recordings\video-1.webm while the updated assertion expects recordings/video-1.webm. The test has never failed in 115 prior runs, and it fails on every browser on Windows — explainable everywhere, not engine-specific. Normalizing the emitted path to / (or asserting with path.sep) fixes it.

Pre-existing flake / infra

• [chrome] › mcp/annotate.spec.ts:173 › user-initiated annotate downloads zip with feedback.md (also [webkit] on Windows) — pre-existing flake. Across the results DB this test failed on unrelated PRs devops: report CI test results as parquet artifacts #41669, devops(test-results-db): CLI to compact CI test results into DuckDB #41673 and feat(routing): add page.routeFromCache / context.routeFromCache #41685 (webkit/firefox on macOS), on SHAs this PR can't be responsible for. This PR only touches video path handling, which the annotate download flow doesn't exercise.
• [webkit] › mcp/dashboard.spec.ts:125 › daemon show: closing page exits the process — pre-existing flake. Failed on unrelated PRs fix(webview): support input for elements inside cross-origin <iframe> #41463, feat(mcp): always pass noDefaults for CDP connections #41676, feat(webkit): roll to r2327 #41684, test(clock): unflake "while running" page-clock tests #41689 and a push run, mostly webkit/firefox on macOS. Unrelated to video path handling.

[github-actions]

Test results for "MCP"

2 failed
❌ [chrome] › mcp/annotate.spec.ts:230 › should capture annotations via show --annotate @mcp-macos-latest-chrome
❌ [chromium] › mcp/cli-killall.spec.ts:42 › kill-all kills filtered dashboard pid @mcp-macos-latest-chromium

7720 passed, 1248 skipped

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Merge workflow run.