[WIP] Update Playwright coverage for role-first play without names

[Codex]

Thanks for asking me to work on this. I will get started on it and keep this PR's description up to date as I form a plan and make progress.

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This section details on the original issue you should resolve

<issue_title>E2E coverage for unnamed, ordered, role-first play</issue_title>
<issue_description>## Summary
Update Playwright coverage for role-first play without relying on player names.

Acceptance criteria

• Existing name-dependent tests are updated to use stable selectors or seat labels.
• Add coverage for starting without names, duplicate role labels, seat-based night kills, seat-based day elimination, role order preservation, Fox trio adjacency, and power-status night skipping.
• Verification includes npm run build, npm run lint, and npm run test:e2e.</issue_description>

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