Web search: configured API providers lose their fallback in DuckDuckGo-unreachable networks — tail the chain with Bing instead? #6746

Summary

For a configured API search provider (tavily, bocha, metaso, …), the backend chain ends in a DuckDuckGo tail. DuckDuckGo's internal Bing fallback only covers empty results / bot challenges — it does not cover connection failure. In networks where DuckDuckGo is unreachable (common behind the GFW and some corporate egresses), the whole chain ends in ToolError::not_available("web search backends unavailable: <id>, duckduckgo") even though Bing itself is reachable, and the provider's legitimate results are thrown away.

Evidence (current main)

• crates/tui/src/tools/web/backend.rs SearchBackendChain::from_context (~114–130): chain is [native?] → configured → SearchProvider::DuckDuckGo tail.
• crates/tui/src/tools/web_search.rs run_scrape_search_with_endpoints (~1560+): the DDG GET's .send() error returns immediately; the internal Bing fallback only runs after a successful response with empty results/challenge. So a DDG connection failure never reaches Bing.
• The tool description still documents "visibly degrade through DuckDuckGo then Bing", which today only holds for the empty/challenge case.

Proposal (from the Pinvou fork, commit ff299f94b)

For the configured-API-provider chain, push the keyless tail from DuckDuckGo down to Bing (the same tail native/explicit chains already use), keeping DuckDuckGo in the chain wherever it is genuinely selectable. This changes deliberately documented fallback behavior, so we're opening a discussion first rather than a PR — alternatives we're happy to consider:

• make the tail provider configurable ([search] fallback_provider);
• try DDG first but fall through to Bing on connection-class errors only;
• keep status quo and document the limitation.

We have a working patch (~10-line core + a chain-shape test per provider) and measured it restoring results in a DDG-blocked network. Happy to send it whichever way maintainers prefer.