F5: web search/fetch on the Kimi services (kimi-cli parity)

web_search now speaks the Kimi search service (kimi-cli tools/web/search.py,
wire-verified against api.kimi.com):
- POST {coding_base}/search with {text_query, limit 1-20 (default 5),
  enable_page_crawling, timeout_seconds: 30}, OAuth bearer +
  X-Msh-Tool-Call-Id; results render in kimi-cli's Title/Date/URL/Summary
  schema with result URLs as citations.
- The old implementation called the xAI Responses API with a search model;
  that client is fully replaced and the entire model-based config surface
  is excised root-and-branch: web_search_model config keys/env/CLI plumbing,
  resolve_web_search_sampling_config, toolset web_search SamplerConfig,
  RemoteSettings.web_search_model, default_web_search_model.
- Enablement is now purely structural: the service exists only on the Kimi
  Code subscription channel, so OAuth sessions get Enabled and API-key-only
  sessions get Disabled (tool absent) — per PRD F5.

web_fetch gains the Kimi fetch service as its primary path (kimi-cli
tools/web/fetch.py): POST {coding_base}/fetch with {url}, Accept:
text/markdown, OAuth bearer + X-Msh-Tool-Call-Id; the 200 body is the
extracted markdown (still overflow-budgeted). Any service failure falls
back to the existing local pipeline (SSRF guards, cache, extraction).
The tool gate defaults ON now (kimi-cli always offers FetchURL) and the
egress User-Agent no longer claims grok-agent/x.ai.

Verified end-to-end against the scripted mock service: a headless session
drove web_search (limit/crawling/call-id observed on the wire) then
web_fetch (Accept + call-id observed) to completion.

crates/codegen/kigi-tui/docs/user-guide/11-custom-models.md

@@ -277,34 +277,6 @@ When you set `models_base_url`, Grok uses API key auth (`Authorization: Bearer`)
 
 ---
 
-## Web Search Model
-
-The `web_search` tool uses a separate model. Configure it with:
-
-```toml
-[models]
-web_search = "grok-4.20-multi-agent"
-```
-
-Or via environment variable:
-
-```bash
-export KIGI_WEB_SEARCH_MODEL="grok-4.20-multi-agent"
-```
-
-If you point web search at a custom model, you also need a `[model.*]` entry so Grok can reach it. Server-side ("backend") web search runs only when the model sets `supports_backend_search = true` (and the build enables backend search); it does not depend on `api_backend`:
-
-```toml
-[models]
-web_search = "my-custom-model"
-
-[model.my-custom-model]
-model = "my-custom-model"
-supports_backend_search = true
-```
-
----
-
 ## Using Custom Models
 
 ```bash