web_search: add searxng provider

docs/reference/api-usage-costs.md

@@ -62,11 +62,12 @@ You can keep it local with `memorySearch.provider = "local"` (no API usage).
 
 See [Memory](/concepts/memory).
 
-### 4) Web search tool (Brave / Perplexity via OpenRouter)
+### 4) Web search tool (Brave / Perplexity / SearXNG)
 `web_search` uses API keys and may incur usage charges:
 
 - **Brave Search API**: `BRAVE_API_KEY` or `tools.web.search.apiKey`
 - **Perplexity** (via OpenRouter): `PERPLEXITY_API_KEY` or `OPENROUTER_API_KEY`
+- **SearXNG** (self-hosted): `tools.web.search.searxng.baseUrl` or `SEARXNG_BASE_URL` (no external API billing; depends on your instance)
 
 **Brave free tier (generous):**
 - **2,000 requests/month**