Define and introduce end-to-end testing with Playwright

### Description

Evaluate and introduce a maintainable end-to-end testing strategy for critical user flows, with Playwright as the expected starting point.

### Action Items

- [ ] Refine the scope after #732 establishes unit-test conventions and initial coverage.
- [ ] Identify the highest-value, stable user journeys and the required test data/environment boundaries.
- [ ] Evaluate Playwright configuration, browser coverage, local developer experience, CI runtime, and test isolation.
- [ ] Define an approach for authentication, external services, fixtures, and deterministic seeded data.
- [ ] Implement a minimal, representative smoke suite only after the strategy is approved.
- [ ] Define artifact retention for failures, including traces, screenshots, and videos, with appropriate privacy controls.
- [ ] Decide when E2E tests may become required and document flake-management and ownership practices.

### Additional Information

Status: Triage — this is intentionally not implementation-ready. Refine the user-flow scope, environment strategy, and CI cost before work begins.

Dependency: #732 (unit testing and initial coverage).

Start by reviewing dependency #732 and the issue's action items. Define the critical user-flow scope, environment and test-data boundaries, Playwright configuration, browser coverage, CI cost, isolation, authentication, external services, artifacts, and ownership practices. Done means an approved maintainable E2E strategy and a minimal smoke-suite plan; implementation is explicitly deferred until that strategy is approved.

Written by the indexing model from the issue text.