Default unmanaged Claude launches to system.ai parent schema

[andy-xu-db]

Plain unmanaged ug claude previously omitted the parent-schema header and relied on the gateway's implicit default. Set parent_schema to system.ai when Claude launches without a managed config, model location, or explicit/saved provider. This uses the existing scoped model discovery and picker path; managed sources and other agents retain their existing behavior.

Add CLI regression coverage and strengthen the configured/fresh Claude integration journeys to assert the generated Databricks-Model-Service-Parent-Schema: system.ai header.

Validation:

• uv run --frozen pytest tests/test_cli.py -q: 412 passed. The new fallback regression fails against the base revision (07b0a8b6) and passes with this change.
• Remaining tests (--ignore=tests/test_e2e.py --ignore=tests/test_cli.py): 2,748 passed, 6 workspace-dependent tests skipped, 4 failures. All four Claude/Codex header-capture failures reproduce on unchanged main: the locally installed agents never contact the capture server.
• CI lint gates pass: Ruff check and format check for src/ tests/, plus ty check src/. Integration contract checks: 37 passed; runner help and formatting also pass. The additional runner lint check reports two pre-existing TID251 violations in scripts/run_integration.py, verified against the base revision.
• Live workspace integration journeys were not run locally; no Databricks profile was selected.