Add frontend unit tests for PublicProjectService

### Task Summary
The frontend service at `frontend/src/app/dashboard/service/user/public-project/public-project.service.ts` currently has no unit-test coverage. Add a spec covering the getType, makePublic, makePrivate, list and add endpoints, including request methods and bodies, exercising both success and error paths.
### Task Type
- [x] Testing / QA

Start by reading frontend/src/app/dashboard/service/user/public-project/public-project.service.ts and identify the getType, makePublic, makePrivate, list and add requests. Add a unit-test spec that checks each request method and body, with both successful responses and error paths; done means the complete endpoint behavior is covered.

Written by the indexing model from the issue text.