refactor: streamline chat flow and improve diagnostics

Store server.log inside OLLAMA_WEB_DATA_DIR and manage the ollama-web file handler through the Starlette lifespan. Close and detach the handler on shutdown to prevent duplicate records and Windows file locks when applications are recreated.

Stop converting DuckDuckGo provider failures into empty search results. Record a query-safe traceback, re-raise the original exception, and let ToolRegistry expose the exception type and message as a tool error without adding or spoofing Referer headers.

Remove the unused non-streaming chat_with_tools implementation and its private helpers. Move capability, options, standard tool, MCP tool, and final tools=[] regression coverage onto the production streaming path.

Add integration coverage for data/server.log placement, handler cleanup, repeated lifespans, and provider 403 diagnostics. Update the Unreleased changelog entry.

Validated with 118 tests, Ruff, mypy, diff checks, real DuckDuckGo searches, successful result-page fetches, and observable 401/403 responses from sites that reject automated retrieval.

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