feat(web): delegate backend availability check to plugin registry for unknown backends

[Josh-OK]

Problem

_is_backend_available() in web_tools.py is a hardcoded whitelist of backend names. Any plugin-registered backend (e.g., crawl4ai, future extract-only providers) is silently rejected because the function doesn't recognize its name — even though the plugin has already registered via PluginContext.register_web_search_provider() with its own is_available() check.

This means setting web.extract_backend: crawl4ai in config has no effect unless someone first patches _is_backend_available() to add a per-backend block. Every new extract-only plugin would need its own hardcoded entry.

Fix

Add a fallthrough at the bottom of _is_backend_available(): when the backend name doesn't match any hardcoded entry, ask the provider registry whether a plugin has registered a provider for that name, and delegate to provider.is_available().

Why this approach

• One change, all plugins: No per-backend special cases in core. Any plugin that registers via register_web_search_provider() works automatically.
• Plugin owns its check: The plugin's own is_available() (which it implements via the WebSearchProvider ABC) is the authority — core doesn't need to know about specific packages or env vars.
• Matches existing pattern: ddgs already checks package importability. This is the same idea, generalized to the plugin registry.
• Minimal surface: 11 lines, no new imports at module level, lazy import prevents circular dependency.

Tested

Verified end-to-end on a host with the crawl4ai plugin registered. Backward-compatible: the hardcoded checks run first and are unchanged. The fallthrough only fires for names not already recognized.

[alt-glitch]

This was generated by AI during triage.

Duplicate of #36987 — both add the same plugin-registry fallthrough (get_provider(backend).is_available()) at the same single call site in _is_backend_available(). #36987 is the earlier/canonical PR. This gate has a saturated competing-fix cluster (#36987, #56201, #32465, #35327 …) against anchor issue #31873; #56201 is the broader 3-site superset.

[kshitijk4poor]

Superseded by #57779, which fixes this same bug class (plugin-registered web providers invisible to the tool-availability gate) as a single chokepoint in _is_backend_available() on current main — cascading to _get_backend(), _get_capability_backend(), and check_web_api_key().

Your PR targeted the same gate and informed the approach — thanks for the contribution, credited in the merged PR body. Closing as superseded. #57779