Move contract interface types (ThresholdParameters, protocol states) to contract-interface crate for Participants BTreeMap migration

[pbeza]

Background

PR #1861 changes Participants from Vec<(AccountId, ParticipantId, ParticipantInfo)> to BTreeMap<AccountId, ParticipantData> for O(log n) lookups. To maintain JSON backward compatibility, we need to introduce DTO serialization types (ParticipantId, ParticipantInfo, ParticipantData, ParticipantsJson, ParticipantsField, ParticipantsJsonDeserialize) in the contract-interface crate.

As identified in Kevin's review, we need to:

1. Use the DTO types in the actual contract interface — the contract should no longer serialize Participants directly; instead, it should convert to the DTO type via an .into_dto_type() (or similar) method.
2. Move additional types to contract-interface — Participants is embedded in ThresholdParameters, which appears in the protocol contract states (Running, Initializing, Resharing), which are returned by the state() view function. These types must also be represented in the contract-interface crate to ensure backward compatibility is enforced at the DTO boundary.

This is significant but mostly mechanical/boilerplate work — defining DTO mirrors of the internal types and wiring up conversions.

User Story

As a contract developer, I need all types that appear in contract method inputs/outputs to be defined in the contract-interface crate, so that internal type changes (like the Participants Vec→BTreeMap migration in #1861) cannot accidentally break the JSON API.

Acceptance Criteria

• The Participants DTO types from feat(dtos): add Participants JSON serialization types to contract-interface #1990 are used in the contract's public interface (not the internal Participants struct)
• An .into_dto_type() (or From/Into impl) conversion exists from internal Participants to the DTO type
• ThresholdParameters (or its DTO equivalent) is defined in contract-interface
• Protocol state types (Running, Initializing, Resharing) that are returned by the state() view function have DTO representations in contract-interface
• The state() view function serializes using the DTO types, not the internal types
• Existing JSON output format is preserved (backward compatible) — validated by unit tests

Resources & Additional Notes

• Parent PR: #1861 — feat: change Participants from Vec to BTreeMap
• DTO types PR: #1990 — feat(dtos): add Participants JSON serialization types to contract-interface
• Kevin's review comment with full context on the contract-interface crate purpose and required work: #1990 review
• The contract-interface crate's purpose: ensure backward compatibility by having all contract I/O types defined there, decoupled from internal types
• This is largely boilerplate work and a good candidate for LLM-assisted development (per Kevin's note)