refactor: migrate identity module to TS

[jaissica12]

Background

• The identity.js module was one of the remaining JavaScript files in the SDK. As part of the ongoing TypeScript migration effort (SDKE-1103), it needed to be converted to TypeScript to improve type safety and maintainability. This is a direct migration with no behavior, API, or breaking changes.

What Has Changed

• Renamed src/identity.js to src/identity.ts with type annotations added to all functions, parameters, and variables
• Corrected pre-existing type mismatches in identity.interfaces.ts, identityApiClient.ts, persistence.interfaces.ts, store.ts, and mp-instance.ts where interfaces didn't match actual runtime behavior
• Updated test files to align with corrected interface types
• No runtime logic, public API, or deprecated behavior was changed — compiled output is functionally identical

Screenshots/Video

• {Include any screenshots or video demonstrating the new feature or fix, if applicable}

Checklist

• I have performed a self-review of my own code.
• I have made corresponding changes to the documentation.
• I have added tests that prove my fix is effective or that my feature works.
• I have tested this locally.

Additional Notes

• {Any additional information or context relevant to this PR}

Reference Issue (For employees only. Ignore if you are an outside contributor)

• Closes https://go/j/SDKE-1103

[sonarqubecloud]

Quality Gate failed

Failed conditions
3.0% Duplication on New Code (required ≤ 3%)

See analysis details on SonarQube Cloud