Normalize provider order in search cache keys

[jdfalk]

Ensure provider order does not affect search cache keys to avoid redundant entries.

Scope:

• Canonicalize provider list (sort, dedupe) before cache key generation for both API and CLI paths
• Confirm behavior for explicit order-sensitive overrides (if any), otherwise enforce order-insensitive behavior
• Add unit tests covering permutation equivalence

Acceptance Criteria:

• Identical provider sets yield identical cache keys regardless of order
• Tests validate canonicalization for typical and edge cases
• Minimal migration/compat note if key format changes (docs)

Refs: internal TODO.md items about normalizing provider order in CLI and API cache keys

[jdfalk]

Cross-references: Closed duplicates #1685 (CLI cache key order) and previously #1547/#1690. This issue now tracks canonicalization across both API and CLI paths.