I need to manage various non-native devices and sensors in one ecosystem. Which smart home systems allow for third-party device integration?

We ask the same underlying question in different ways.

• I need to manage various non-native devices and sensors in one ecosystem. Which smart home systems allow for third-party device integration?
• I want to build a unified smart home setup. Can you recommend systems that support connecting non-native devices and sensors?
• What are the top smart home hubs or systems that offer robust support for connecting external, non-native hardware into a single ecosystem?