feat(sse): add Notion AI Web (Unofficial/Experimental) provider (#6758) (#7600)

Notion AI has no public inference API (see closed request #3272), so this
adds it as a new entry in the established web-cookie provider category
(chatgpt-web, claude-web, grok-web, ...): cookie-based auth via the
token_v2 session cookie posted to Notion's undocumented internal
POST /api/v3/runInferenceTranscript endpoint, translating its NDJSON
transcript-patch stream into OpenAI-compatible chat completions.

- NotionWebExecutor (open-sse/executors/notion-web.ts): resolves the
  token_v2 cookie (+ optional space_id/notion_browser_id), builds a
  Notion transcript from the chat messages, parses the NDJSON response
  (cumulative-snapshot semantics, mirroring gemini-web.ts's handling of
  #7163), and returns a chat.completion or pseudo-streamed SSE response.
  All error paths route through makeExecutorErrorResult (sanitized).
- RegistryEntry under open-sse/config/providers/registry/notion-web/,
  registered in providers/index.ts REGISTRY and executors/index.ts
  (alias "nw").
- WEB_COOKIE_PROVIDERS entry (src/shared/constants/providers/web-cookie.ts)
  with subscriptionRisk + webCookie risk notice, clearly labeled
  "(Unofficial/Experimental)".
- Cookie-probe validator (validateNotionWebProvider) against Notion's
  getSpaces endpoint, and a webSessionCredentials.ts UI entry for the
  "Add session cookie" flow.
- Regenerated docs/reference/PROVIDER_REFERENCE.md and the
  provider/translate-path golden snapshot (purely additive diffs); synced
  the "251 providers" count across README/AGENTS/CLAUDE.md
  (check:docs-counts STRICT gate).

Tests: tests/unit/executor-notion-web.test.ts (22 cases — registry
consistency, mocked-upstream request/response translation, NDJSON
snapshot parsing, cookie resolution, sanitized error paths) plus the
existing executor-web-cookie-sweep, provider-alias-uniqueness,
check-provider-consistency, web-session-credentials, and
provider-translate-path-golden suites all pass with notion-web included.

docs/reference/PROVIDER_REFERENCE.md

@@ -58,7 +58,7 @@ Use the dashboard at `/dashboard/providers` to enable, configure, and test each
 | `zed` | `zd` | Zed IDE | OAuth | [link](https://zed.dev) | Zed stores LLM provider credentials (OpenAI, Anthropic, Google, Mistral, xAI) in the OS keychain. Use the Import button below to discover and import them automatically. |
 | `zed-hosted` | — | Zed Hosted Models | OAuth | [link](https://zed.dev) | Sign in with your Zed account (native-app sign-in). OmniRoute generates a one-time RSA keypair and opens zed.dev to authorize it — on a remote/headless install, copy the resulting 127.0.0.1 callback URL from your browser's address bar and paste it back here. Distinct from the 'Zed IDE' credential-import entry above: this proxies chat completions through Zed's own hosted model aggregator (cloud.zed.dev), fronting Anthropic/OpenAI/Google/xAI models under your Zed plan. |
 
-## Web Cookie Providers (25)
+## Web Cookie Providers (26)
 
 | ID | Alias | Name | Tags | Website | Notes |
 |----|-------|------|------|---------|-------|
@@ -78,6 +78,7 @@ Use the dashboard at `/dashboard/providers` to enable, configure, and test each
 | `kimi-web` | `kimi-web` | Kimi Web (Moonshot AI) | Web cookie | [link](https://www.kimi.com) | Paste your Cookie header from www.kimi.com (must contain kimi-auth=...). Find it via DevTools → Network → request → Cookie. |
 | `lmarena` | `lma` | Arena (Free) | Web cookie | [link](https://arena.ai) | Paste the full Cookie header from arena.ai (DevTools → Network → request → Cookie). Include arena-auth-prod-v1.0/.1… and cf_clearance/__cf_bm when present. OmniRoute uses Chrome TLS impersonation; if Arena still 403s, set providerSpecificData.recaptchaV3Token from a live browser session. |
 | `muse-spark-web` | `ms-web` | Muse Spark Web (Meta AI) | Web cookie | [link](https://www.meta.ai) | Paste your ecto_1_sess value or full cookie header from meta.ai |
+| `notion-web` | `nw` | Notion AI Web (Unofficial/Experimental) | Web cookie | [link](https://www.notion.so) | Paste your token_v2 cookie value from notion.so (DevTools → Application → Cookies). Optionally append `; space_id=...` and/or `; notion_browser_id=...` if your workspace requires them. |
 | `perplexity-web` | `pplx-web` | Perplexity Web (Pro/Max) | Web cookie | [link](https://www.perplexity.ai) | Paste your __Secure-next-auth.session-token cookie value from perplexity.ai |
 | `poe-web` | `poe` | Poe Web (Subscription) | Web cookie | [link](https://poe.com) | Paste your p-b cookie value from poe.com (DevTools → Application → Cookies → p-b) |
 | `qwen-web` | `qwen-web` | Qwen Web (Free) | Web cookie | [link](https://chat.qwen.ai) | Open chat.qwen.ai, log in, then open DevTools → Application → Local Storage → copy the "token" value (or use tongyi_sso_ticket cookie as Bearer token). |