Adds SearXNG as a free, self-hosted web search provider. SearXNG is a
privacy-respecting metasearch engine that requires no API key — just a
running instance and SEARXNG_URL pointing at it.
## What this adds
- `tools/web_providers/searxng.py` — `SearXNGSearchProvider` implementing
`WebSearchProvider` (search only; no extract capability)
- `_is_backend_available("searxng")` — gates on SEARXNG_URL
- `_get_backend()` — accepts "searxng" as a configured value; adds it to
auto-detect candidates (lower priority than paid services)
- `web_search_tool` — dispatches to SearXNG when it is the active backend
- `check_web_api_key()` — includes SearXNG in availability check
- `OPTIONAL_ENV_VARS["SEARXNG_URL"]` — registered with tools=["web_search"]
- `tools_config.py` — SearXNG appears in the `hermes tools` provider picker
- `nous_subscription.py` — `direct_searxng` detection, web_active / web_available
- `setup.py` — SEARXNG_URL listed in the missing-credential hint
- 23 tests covering: is_configured, happy-path search, score sorting, limit,
HTTP/request errors, _is_backend_available, _get_backend, check_web_api_key
## Config
```yaml
# Use SearXNG for search, any paid provider for extract
web:
search_backend: "searxng"
extract_backend: "firecrawl"
# Or: SearXNG as the sole backend (web_extract will use the next available)
web:
backend: "searxng"
```
SearXNG is search-only — it does not implement WebExtractProvider. Users
who only configure SEARXNG_URL get web_search available; web_extract falls
back to the next available extract provider (or is unavailable if none).
Closes#19198 (Phase 2 Task 4 — SearXNG provider)
Ref: #11562 (original SearXNG PR)
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