test(playground): exercise SSE reconnect Last-Event-ID replay

[MarioCadenas]

Why

The existing reconnect E2E tests in apps/dev-playground/tests/reconnect.spec.ts only cover the happy path. They install setupMockAPI, which fulfills /api/reconnect/stream with a static SSE body delivering all 5 messages at once — the connection is never actually dropped. As a result, the real server reconnection path (StreamManager ring-buffer replay via Last-Event-ID, packages/appkit/src/stream/stream-manager.ts) was never exercised end-to-end. That blind spot is exactly why a real reconnect regression could survive ~6 weeks: a broken replay would still pass every existing test.

What

Adds one recovery test (kept alongside, not replacing, the happy-path tests) in a separate describe block so it runs against the real dev-playground server (no stream mock):

• Loads /reconnect, waits until some (≥1, <5) messages have arrived.
• Forces a client-side disconnect mid-stream with context.setOffline(true) then setOffline(false), which aborts the in-flight SSE fetch and triggers the client's reconnect with a Last-Event-ID header against the same streamId.
• Asserts the stream completes with all 5 messages (headline reads 5), status never reaches Error, and the rendered list contains exactly one Message k/5 card for each k in 1..5 — i.e. no gaps and no duplicates, which is what proves the server replayed the buffered events the client missed.

Assertions use Playwright web-first / expect.poll with generous timeouts (no arbitrary sleeps beyond the brief offline window) to keep the SSE timing robust. The test is annotated scenario: reconnect-replay for triage.

Verification

Ran locally against the real server (reproducing CI env: APPKIT_E2E_TEST=true + mock workspace vars), Playwright auto-starting the server:

• Full reconnect.spec.ts: 4 passed (new recovery test ~13s).
• Recovery test --repeat-each=3: 3/3 passed, stable ~12.8s — no flakiness observed.
• False-green check: temporarily disabled the missed-event replay loop in StreamManager._attachToExistingStream and confirmed the new test fails (stalls at 4 messages, never reaches 5), proving it genuinely catches a replay regression. Reverted afterwards.

Biome clean; no new lint errors. The playground-integration-test CI job will also execute this.

This pull request and its description were written by Isaac.