[codex] use supported-only provider matrix

[luca-ctx]

Summary

• simplify the public provider matrix to one supported term: supported
• remove public proof/tier fields and keep detailed evidence in ctx-private
• keep Rust deserialization tolerant for old rows while the public checker rejects legacy public status vocabulary

Verification

• python3 scripts/check-provider-support-matrix.py
• cargo test -p ctx-history-core provider_support_matrix
• cargo test -p ctx --test cli_public_help_docs docs
• bash scripts/check-docs.sh
• cargo fmt --all -- --check
• git diff --check

Review Notes

• Rebased on latest origin/main before push.
• This is the public companion for the ctx-private provider proof parity gate.