docs+skill: add searxng-search optional skill and documentation

Closes the remaining gaps from PR #11562 that weren't covered by the
core SearXNG integration landed in #20823.

- optional-skills/research/searxng-search/ — installable skill with
  SKILL.md (curl-based usage, category support, Python example) and
  searxng.sh helper script for health checks and instance queries
- website/docs/user-guide/configuration.md — SearXNG added to the
  Web Search Backends section (5 backends, backend table, per-capability
  split config example, correct search-only note)
- website/docs/reference/environment-variables.md — SEARXNG_URL row
- website/docs/reference/optional-skills-catalog.md — searxng-search entry

The core SearXNG code, OPTIONAL_ENV_VARS, hermes tools picker, and tests
were already on main via #20823.  This commit is purely additive docs +
the optional skill scaffold.

Credits from #11562 salvage:
  @w4rum — original _searxng_search structure
  @nathansdev — tools_config.py integration
  @moyomartin — category support and result formatting
  @0xMihai — config/env var approach
  @nicobailon — skill and documentation structure
  @searxng-fan — error handling patterns
  @local-first — self-hosted-first philosophy and docs

website/docs/reference/environment-variables.md

@@ -120,6 +120,7 @@ For native Anthropic auth, Hermes prefers Claude Code's own credential files whe
 | `FIRECRAWL_API_KEY` | Web scraping and cloud browser ([firecrawl.dev](https://firecrawl.dev/)) |
 | `FIRECRAWL_API_URL` | Custom Firecrawl API endpoint for self-hosted instances (optional) |
 | `TAVILY_API_KEY` | Tavily API key for AI-native web search, extract, and crawl ([app.tavily.com](https://app.tavily.com/home)) |
+| `SEARXNG_URL` | SearXNG instance URL for free self-hosted web search — no API key required ([searxng.github.io](https://searxng.github.io/searxng/)) |
 | `TAVILY_BASE_URL` | Override the Tavily API endpoint. Useful for corporate proxies and self-hosted Tavily-compatible search backends. Same pattern as `GROQ_BASE_URL`. |
 | `EXA_API_KEY` | Exa API key for AI-native web search and contents ([exa.ai](https://exa.ai/)) |
 | `BROWSERBASE_API_KEY` | Browser automation ([browserbase.com](https://browserbase.com/)) |

website/docs/reference/optional-skills-catalog.md

@@ -143,6 +143,7 @@ hermes skills uninstall <skill-name>
 | [**domain-intel**](/docs/user-guide/skills/optional/research/research-domain-intel) | Passive domain reconnaissance using Python stdlib. Subdomain discovery, SSL certificate inspection, WHOIS lookups, DNS records, domain availability checks, and bulk multi-domain analysis. No API keys required. |
 | [**drug-discovery**](/docs/user-guide/skills/optional/research/research-drug-discovery) | Pharmaceutical research assistant for drug discovery workflows. Search bioactive compounds on ChEMBL, calculate drug-likeness (Lipinski Ro5, QED, TPSA, synthetic accessibility), look up drug-drug interactions via OpenFDA, interpret ADMET... |
 | [**duckduckgo-search**](/docs/user-guide/skills/optional/research/research-duckduckgo-search) | Free web search via DuckDuckGo — text, news, images, videos. No API key needed. Prefer the `ddgs` CLI when installed; use the Python DDGS library only after verifying that `ddgs` is available in the current runtime. |
+| [**searxng-search**](/docs/user-guide/skills/optional/research/research-searxng-search) | Free meta-search via SearXNG — aggregates results from 70+ search engines. Self-hosted or use a public instance. No API key needed. Falls back automatically when the web search toolset is unavailable. |
 | [**gitnexus-explorer**](/docs/user-guide/skills/optional/research/research-gitnexus-explorer) | Index a codebase with GitNexus and serve an interactive knowledge graph via web UI + Cloudflare tunnel. |
 | [**parallel-cli**](/docs/user-guide/skills/optional/research/research-parallel-cli) | Optional vendor skill for Parallel CLI — agent-native web search, extraction, deep research, enrichment, FindAll, and monitoring. Prefer JSON output and non-interactive flows. |
 | [**qmd**](/docs/user-guide/skills/optional/research/research-qmd) | Search personal knowledge bases, notes, docs, and meeting transcripts locally using qmd — a hybrid retrieval engine with BM25, vector search, and LLM reranking. Supports CLI and MCP integration. |