Can new Health-app fields be created by 3rd parties?
Neither you nor third-party developers can add fields to Health.

Working with the HealthKit Framework
The HealthKit framework is designed to share data between apps in a meaningful way. The framework constrains the types of data and units to a predefined list, ensuring that all apps understand what the data means and how it can be used. Developers cannot create custom data types or units. Instead, HealthKit provides a wide variety of data types and units.

HealthKit | Apple Developer Documentation