Split from PR #2752 (part 3 of 3).
Backend:
- /api/models/{index}/test endpoint for testing saved model configs
- /api/models/test-inline endpoint for testing unsaved form values
- Real network probe (GET /models) for connectivity verification
- Credential reuse with provider/API base matching for security
- Default API base resolution for providers without explicit base
Frontend:
- TestModelDialog for testing model connectivity
- Inline test support for add/edit model sheets
- Static import for TestModelDialog (replaces dynamic import from PR1)
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