test(e2e): make clean full-suite runs match sharded CI

[tiankaima]

Problem

A clean-database local run of the documented full Playwright suite does not match the repository's canonical sharded GitHub Actions result.

On d6e8426e:

• fresh database, all 49 migrations applied;
• canonical seed completed;
• production build completed;
• bunx playwright test: 658 passed, 53 failed, 1 skipped, 29 did not run (741 total);
• the same commit's four GitHub Actions E2E shards all passed.

A prior run after integration tests produced almost the same result (657 passed, 54 failed), so integration-database contamination is not the main explanation.

Observed failure clusters include dashboard Todo state transitions, OAuth device token/scope cases, mobile section homework forms, welcome/profile validation, and mobile welcome screenshot coverage.

Why this matters

The unsharded local command currently cannot be used as an independent release gate or to reproduce the combined suite. Passing only under CI sharding can hide order dependence, shared fixture state, worker/port assumptions, or missing local orchestration.

Acceptance criteria

• Identify whether the divergence is test-order pollution, worker concurrency, server/database lifecycle, shard-specific setup, or a documented environment requirement.
• Add a reproducible clean-database command for the complete suite.
• Make the complete local run and the union of CI shards execute equivalent setup and test coverage.
• Fix order/shared-state dependencies or explicitly isolate affected projects.
• Add a CI smoke/check that prevents the supported full-suite command from silently drifting.
• Document expected artifact/report locations and cleanup.

Scope note

This was discovered while validating #605. Its GraphQL/MCP changes do not touch the failing UI/auth surfaces, and #605's canonical sharded CI passed.