Add dedicated web E2E test gate before re-enabling Playwright in just test-all

[ifsheldon]

Problem

just test-all previously depended on test-web-e2e, which ran cd frontends/web && bunx playwright test directly. The web app does not currently have a dedicated Playwright E2E config, fixture strategy, or stable E2E command, so this is not a reliable MVP release gate. It can pick up the wrong files or fail for setup reasons unrelated to the MVP smoke surface.

For MVP, just test-all should stay limited to the reliable Rust and frontend unit gates.

Proposed solution

Add a dedicated web E2E setup before wiring Playwright back into the default gate:

• Add an explicit Playwright config for Agentics web E2E.
• Put E2E specs under a dedicated directory such as frontends/web/e2e/.
• Define a package script, for example bun run test:e2e, that starts or targets the correct web server.
• Use stable fixtures and explicit auth/session setup for admin, creator, public, and agent-facing views.
• Re-enable a just test-web-e2e target only after the command is reliable locally and in CI.

Alternatives and tradeoffs

• Keep Playwright out of test-all until after MVP: fastest and least noisy, but browser regressions rely on targeted/manual checks.
• Add a single smoke-only Playwright test now: catches basic routing issues, but may still create a false sense of coverage if auth and data setup are not stable.
• Build the full E2E harness now: best long-term quality, but too much release-gate work for the current MVP polish pass.

Acceptance criteria

• frontends/web has a dedicated Playwright config and E2E test directory.
• The E2E command is documented and deterministic on a clean checkout.
• CI and just test-web-e2e use the same command.
• just test-all includes test-web-e2e only after the E2E command is stable.

[ifsheldon]

Partial progress update:

Agentics now has a production-rehearsal-specific Playwright setup:

• frontends/web/playwright.rehearsal.config.ts
• frontends/web/e2e/production-rehearsal.playwright.ts
• bun run rehearse:e2e

This covers rehearsal observer smoke checks from a generated rehearsal manifest, but it is not yet the stable generic web E2E gate described here. There is still no bun run test:e2e, no just test-web-e2e, and Playwright is intentionally still outside just test-all.

Keeping this open for the remaining generic/local E2E harness and gate decision.