fix: backup keys are on the secp256k1 curve

[paolodamico]

The backend was incorrectly verifying backup account keys on the P256 curve. See https://github.com/worldcoin/bedrock/blob/d15b20a65d452cc974b45d17c0f1f753921bfb4b/bedrock/src/root_key/mod.rs#L210

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Note

Medium Risk
Changes cryptographic signature verification for the reset flow from p256 to k256 (secp256k1), which can affect account recovery behavior if key parsing/signature validation differs.

Overview
Fixes reset signature verification to match backup key curve. The reset route now parses backup_account_id public keys and verifies signatures using k256/secp256k1 rather than p256.

Workspace dependencies were updated to add k256 (and adjust p256 features), and unit/integration tests for reset were updated to generate/sign with secp256k1 keys (including a dedicated helper for backup-key challenge signing).

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[Copilot]

Pull request overview

Fixes the reset/backup recovery flow to verify backup_account_id signatures on the correct curve (secp256k1), aligning backend behavior with how backup keys are generated and represented.

Changes:

• Switch reset signature verification from p256 to k256 (secp256k1) when parsing backup_account_id compressed public keys.
• Update reset unit + integration tests to generate and sign challenges with secp256k1 backup keys.
• Update workspace dependencies to include k256 (and adjust p256 features).

Reviewed changes

Copilot reviewed 3 out of 4 changed files in this pull request and generated 1 comment.

File	Description
src/routes/reset.rs	Uses k256 to parse compressed backup_account_id public keys and verify ECDSA signatures on secp256k1.
tests/reset_backup_integration.rs	Updates reset integration tests to derive backup_account_id and sign challenges using secp256k1 backup keys.
Cargo.toml	Adds k256 dependency and adjusts p256 features in the workspace.
Cargo.lock	Locks k256 and its transitive dependencies.

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