[agent] Make the default Parsar Core connection zero-input and testable

[sam2tom]

Context

The normal local path already uses /v1, proxies to 127.0.0.1:8091, and reads ~/.parsar/agents-api/web-token on the Vite server. The current dialog still asks ordinary users to understand base URLs, Bearer tokens, CORS, key digests, and daemon setup before they can connect.

Observable outcome: a conventional local Parsar setup connects with no user-entered fields, while custom compatible Cores remain available behind an explicit advanced path.

Acceptance criteria

• Present Local Parsar Core as the default connection mode with /v1 fixed by the application.
• When server-managed proxy authentication is active, do not show or request a browser Bearer token.
• Move direct URLs, CORS guidance, and current-tab tokens into an Other compatible Core / Advanced mode.
• Replace the inline key-generation and daemon tutorial with a concise status summary plus links to the operator guide.
• Add an explicit, read-only Test connection action using Agents API GET requests only; it must not create an Agent, Session, Turn, Item, or model call.
• Distinguish unreachable/network-or-CORS, 401 invalid_api_key, beta-header/protocol mismatch, and authenticated basic API access.
• Report execution readiness as Unknown / not verified. HTTP health, Agent CRUD, or an open SSE stream must never be presented as proof that a daemon, model, or provider is ready.
• Invalidate a previous test result whenever the draft mode, URL, or token changes.
• Keep a direct-mode token only in the current tab's sessionStorage; never include it in URLs, logs, error text, snapshots, or persistent storage.
• Cover keyboard, screen-reader, narrow-layout, loading, success, and every failure state.

File ownership

• apps/web/src/components/ConnectionModal.tsx
• apps/web/src/components/ConnectionModal.test.tsx
• new apps/web/src/lib/core-probe.ts and focused tests
• a feature-local stylesheet if needed

Avoid broad edits to App.tsx, apps/web/src/style.css, client protocol types, and README files. Coordinate any unavoidable integration seam before editing a shared hotspot.

Validation

• Run focused connection modal and probe tests.
• Run pnpm check and git diff --check.
• No paid model request is required.

Non-goals

• Do not generate Core keys or daemon credentials in the browser.
• Do not start, stop, migrate, or modify Parsar Core.
• Do not invent a readiness or capability endpoint; upstream gaps remain tracked in [tracking] OpenAI Agents API gaps blocked on Parsar Core #8.
• Do not broaden the current-tab token fallback into a production authentication design.

Dependencies

Use the user journey defined by the bilingual README update. Runtime/model capability discovery remains blocked on #8.