Fixes #13287.

Root cause:
tests/integration/test_web_tools.py looked like a pytest integration module but only exposed a manual script-style harness, so pytest collected zero tests from the file.

Fix summary:

• Add real pytest-collectable wrappers for search, extraction without LLM, extraction with LLM, and crawl flows.
• Keep the manual script entry point intact.
• Gate live web checks behind existing web backend credential detection so default local/CI runs skip safely instead of making unauthenticated external calls.
• Add structure/content assertions for enabled integration runs.

Tests:

• uv run --frozen --python 3.11 --extra dev pytest -o addopts= --collect-only tests/integration/test_web_tools.py -> 4 tests collected
• uv run --frozen --python 3.11 --extra dev pytest -o addopts= tests/integration/test_web_tools.py -q -> 4 skipped
• git diff --check -- tests/integration/test_web_tools.py