After I add Apple Home, how do I add other platforms

First, select "Turn On Pairing Mode" on the device's settings page, and you will get a Setup Code.
You can then add the code manually by entering it into the app on other platforms.
The name of the code may be different for each platform, SmartThings is called "Enable for other services". Amazon calls the same function "Other Assistants and Apps." Google has named it "Link apps & services ".