docs(tools): restructure web tools IA and rewrite web.md

Navigation restructure:
- "Browser" group -> "Web Browser"
- New "Web Tools" group containing Web Fetch, Web Search, and all
  7 search provider sub-pages
- Other tools (btw, diffs, etc.) stay at top level

New page:
- tools/web-fetch.md: dedicated web_fetch reference with Steps,
  config, Firecrawl fallback, limits

Rewritten page:
- tools/web.md: now "Web Search" -- focused search overview with
  Steps quick-start, CardGroup provider picker, Tabs for key storage,
  provider comparison table, auto-detection, parameters, examples.
  Removed all inline provider setup (lives in sub-pages) and web_fetch
  content (now in dedicated page).

Final sidebar:
  Tools
  ├── Web Browser (browser, login, troubleshooting)
  ├── Web Tools
  │   ├── Web Fetch
  │   ├── Web Search
  │   └── Brave / Firecrawl / Gemini / Grok / Kimi / Perplexity / Tavily
  ├── btw, diffs, exec, ...

docs/docs.json

@@ -84,6 +84,10 @@
       "source": "/perplexity",
       "destination": "/tools/perplexity-search"
     },
+    {
+      "source": "/web-fetch",
+      "destination": "/tools/web-fetch"
+    },
     {
       "source": "/gemini-search",
       "destination": "/tools/gemini-search"
@@ -1104,7 +1108,7 @@
                 "pages": [
                   "tools/apply-patch",
                   {
-                    "group": "Browser",
+                    "group": "Web Browser",
                     "pages": [
                       "tools/browser",
                       "tools/browser-login",
@@ -1112,6 +1116,20 @@
                       "tools/browser-wsl2-windows-remote-cdp-troubleshooting"
                     ]
                   },
+                  {
+                    "group": "Web Tools",
+                    "pages": [
+                      "tools/web-fetch",
+                      "tools/web",
+                      "tools/brave-search",
+                      "tools/firecrawl",
+                      "tools/gemini-search",
+                      "tools/grok-search",
+                      "tools/kimi-search",
+                      "tools/perplexity-search",
+                      "tools/tavily"
+                    ]
+                  },
                   "tools/btw",
                   "tools/diffs",
                   "tools/elevated",
@@ -1122,20 +1140,7 @@
                   "tools/loop-detection",
                   "tools/pdf",
                   "tools/reactions",
-                  "tools/thinking",
-                  "tools/web",
-                  {
-                    "group": "Web Search",
-                    "pages": [
-                      "tools/brave-search",
-                      "tools/firecrawl",
-                      "tools/gemini-search",
-                      "tools/grok-search",
-                      "tools/kimi-search",
-                      "tools/perplexity-search",
-                      "tools/tavily"
-                    ]
-                  }
+                  "tools/thinking"
                 ]
               },
               {