feat(search): harvest custom DuckDuckGo endpoint

[Hmbown]

Summary

• Harvests feat(search): allow custom DuckDuckGo endpoint #2510 by @cyq1017 for DuckDuckGo-compatible private search endpoints requested in Support custom URL for search provider #2436 by @Artenx.
• Adds [search].base_url, preferred CODEWHALE_SEARCH_BASE_URL, and legacy DEEPSEEK_SEARCH_BASE_URL support.
• Gates network policy on the configured endpoint host, disables public Bing fallback for custom endpoints, and returns explicit errors for non-DuckDuckGo provider/base_url pairings and challenge pages.
• Polishes diagnostics so custom endpoint results report the configured host in source instead of always duckduckgo.

Credit

Harvested from PR #2510 by @cyq1017.
Reported by @Artenx in #2436.

Verification

• cargo test -p codewhale-tui --all-features --locked custom_duckduckgo -- --nocapture
• cargo test -p codewhale-tui --all-features --locked search_base_url -- --nocapture
• cargo test -p codewhale-tui --all-features --locked search_provider -- --nocapture
• cargo check -p codewhale-tui --all-features --locked
• cargo clippy -p codewhale-tui --all-features --locked -- -D warnings
• cargo fmt --all -- --check
• git diff --check
• ./scripts/release/check-versions.sh
• python3 scripts/check-coauthor-trailers.py --author-map .github/AUTHOR_MAP --range origin/codex/v0.9.0-stewardship..HEAD --check-authors

Fixes #2436.

[greptile-apps]

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[gemini-code-assist]

Code Review

This pull request adds support for custom DuckDuckGo-compatible private search endpoints via the [search].base_url configuration or the CODEWHALE_SEARCH_BASE_URL environment variable. Custom endpoints bypass the public Bing fallback, enforce network policies on their configured host, and report the custom host as the result source. The review feedback suggests validating that the custom base_url uses an http or https scheme to prevent potential runtime errors during request execution.

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[gemini-code-assist]

The custom base_url is parsed using reqwest::Url::parse, but there is no validation to ensure that the scheme is either http or https. If an unsupported scheme (like ftp or file) is configured, it could lead to unexpected runtime errors or failures when reqwest attempts to execute the request. Adding an explicit check for http or https schemes improves robustness.

    let mut url = reqwest::Url::parse(raw).map_err(|err| {
        ToolError::invalid_input(format!(
            "Invalid DuckDuckGo-compatible search base_url: {err}"
        ))
    })?;
    if url.scheme() != "http" && url.scheme() != "https" {
        return Err(ToolError::invalid_input(format!(
            "DuckDuckGo-compatible search base_url must use http or https scheme, got: {}",
            url.scheme()
        )));
    }