feat: implement mid-cycle proration engine

[deedee-code]

Pull Request Checklist

Quality Gates (All must pass before merge)

• Lint: Code passes ESLint and Prettier checks
• Type Check: TypeScript compilation succeeds
• Tests: All tests pass
• Build: Project builds successfully
• Rust Format: Smart contract formatting is correct
• Rust Clippy: Smart contract linting passes
• Rust Tests: All smart contract tests pass
• Rust Build: Smart contracts compile successfully

Additional Requirements

• New code has appropriate TypeScript types
• No hardcoded secrets or credentials
• New features have corresponding tests
• Documentation updated if needed

Closes: #930

Reviewers

• At least 1 approval required for merge
• All CI checks must be green

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This PR will not be mergeable until all quality gates pass.

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