The work to process payments with BLIK was initially implemented in the PoC tracked by #3827. We need to refine and integrate this functionality properly by cleaning up the existing code, placing it behind the feature flag #3953, and adding test coverage.

• Add BLIK behind the feature flag to allow controlled rollouts.
• Clean up the code from the PoC branch to align with best practices and maintainability.
• Implement unit tests to cover the payment processing logic.
• Ensure a simple product can be successfully purchased using BLIK without saving it.