feat: allow web tools to discover plugin-registered backends

[zhanglingfei112]

_is_backend_available() only checks hardcoded backends. Plugin-registered backends via web_search_registry were never detected. Add a fallback check so custom web plugins work.

[alt-glitch]

Duplicate of #31829 — same fix adding registry fallback in _is_backend_available() for plugin-registered web search backends. Also competes with #33516, #31887, #28652. Fixes #31873 / #28651.

[teknium1]

Thanks for the focused plugin-registry fallback contribution. This is now implemented on main through a broader, tested fix, so this PR is superseded.

• tools/web_tools.py:323-327 now resolves non-legacy backend availability through the registered provider's is_available() method.
• tools/web_tools.py:230-266 also accepts configured registered providers and discovers available custom providers when built-ins are unavailable.
• tests/tools/test_web_tools_config.py:697-813 covers custom-provider tool-gate activation, backend selection, per-capability selection, and registry visibility.
• The implementation landed via fix(web_tools): honor plugin-registered provider availability at the tool gate #57779 (merge commit a9cd0e07cbe6f411c875d6cfd3c8c356ca90b121; implementation commit 0a9d42ce402cc1a4e12dee18a313c1db2e0a02e3). The prior duplicate discussion pointing to fix(web_tools): delegate _is_backend_available to provider registry for plugin backends #31829 was also considered.

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