fix(mcp): surface the missing executable path when a browser isn't installed

[dcrousso]

when a browser binary is missing, throwIfExecutableMissing caught playwright-core's Executable doesn't exist at <path> and rethrew a generic Browser "<name>" is not installed, dropping the path

that path holds the version-specific directory (e.g. firefox-1534), which is what tells a genuinely missing install apart from a version mismatch

browsers from a standalone playwright install land in a differently-versioned directory than the bundled playwright-core expects

keep the path in the rethrown message so the mismatch is diagnosable

this is a further improvement for #40867

referenced in #41871

[github-actions]

Test results for "MCP"

1 failed
❌ [chrome] › mcp/cli-core.spec.ts:168 › dialog-accept @mcp-windows-latest-chrome

7794 passed, 1266 skipped

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Merge workflow run.

[github-actions]

Hi, I'm the Playwright bot and I took a first look at the CI failures here.

🟢 The one failure is a pre-existing flake — this PR is clear

[chrome] › mcp/cli-core.spec.ts:168 › dialog-accept failed on mcp-windows-latest-chrome, but it's a known Windows flake, not something this PR caused. The same test failed with the identical error on PR #41909 (sha 7faf1c08), which this PR can't be responsible for. The diff only touches the missing-executable message in browserFactory.ts and tests/mcp/launch.spec.ts — nothing the dialog flow exercises.

Details

Pre-existing flake / infra

• [chrome] › mcp/cli-core.spec.ts:168 › dialog-accept (mcp-windows-latest-chrome) — across the test-results DB this test is bimodal only on Windows and only rarely: chrome passed 164 of 165 runs (the one fail is this PR), and msedge passed 164 of 165 (the one fail was PR fix(mcp): report malformed JSON config instead of falling back to INI #41909, run 29863130236, sha 7faf1c08). Both failures share the exact same signature:

  Error: expect(received).toContain(expected) // indexOf
  Expected substring: "[\"alert\" dialog with message \"MyAlert\"]"
  

  Same test failing on an unrelated SHA is the proof this is flake, not regression. On every non-Windows bot it's 0 failures over 400+ runs each. This PR changes how a missing browser executable is reported (throwIfExecutableMissing in browserFactory.ts) plus a launch test — the dialog-accept path doesn't go anywhere near that code.

_{Triaged by the Playwright bot - agent run}