doctor: show active search provider in codewhale doctor output

Problem

web_search defaults to Bing HTML scraping, which silently returns empty results for technical queries. DuckDuckGo works reliably (see #2130, #964). Users don't discover the [search] config section because:

1. codewhale doctor doesn't mention the active search provider
2. The config.example.toml search section is commented out by default
3. There's no /search slash command to inspect or switch providers

Proposed Fix

Add a search provider line to codewhale doctor output:

Search provider: bing (default; set [search] provider = "duckduckgo" in config.toml to switch)

or when DuckDuckGo is configured:

Search provider: duckduckgo (configured in ~/.deepseek/config.toml)

Acceptance Criteria

• codewhale doctor shows the active search provider with its source (default vs. config)
• Provider line includes a brief hint about switching when on default Bing
• codewhale doctor --json includes search_provider field in output
• When DEEPSEEK_SEARCH_PROVIDER env var is set, doctor shows "env override" source

Stretch (separate PR)

• /search slash command to inspect and switch providers in-session
• codewhale doctor warns when Bing is the active provider ("Bing may return empty results for technical queries")

Related

• #2130 — code-level Bing→DDG fallback
• #964 — original web_search bug report
• #1681 — region-aware search providers