If you are trying to bring the smartthings hub into another matter capable app, my understanding is that will never happen. Smartthings has said publicly that their hubs will not be “matter Bridges” which is what you need for integration out.
Instead, smartthings has opted for one-way matter compatibility in. Its hubs will be “matter controllers” which means you can add matter compatible devices from other companies to your smartthings account.
So there are different possible configurations. It is up to each device manufacturer as far as which of these configurations they choose to use for a hub.
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one-way integration out. This is how the Hue hub will work. You can add it to other matter capable apps, such as Apple home or smartthings, but you cannot bring matter capable devices from other companies in to the hue app using only matter. (you can still add some zigbee devices like INNR and Gledopto to Hue.)
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one-way integration in. This is how the smartthings hub will work. You can add other matter capable devices to Smart things, but you cannot add the smartthings hub to other companies’ matter capable apps.
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two way integration. So far the only company I have seen which has promised this configuration is IKEA with their new dirigera hub, which will be both a matter controller and a matter bridge. But it’s going to take them a few months to get there. You can buy the hub now, but it’s going to take a software update before it will act as a matter bridge. Hopefully they will get there, it’s just not there yet.
So…
If everything was working correctly, you would be able to add a hue hub to your smartthings set up using matter, but you would not be able to add a smartthings hub to the hue app, or to the Apple Home app using matter. You will still need homebridge to get smartthings devices into the Apple home app.
All of that said, that just describes how it’s supposed to work.
There have been reports both in this forum and elsewhere (including in this thread) That so far people cannot add even the example simulated devices to Smartthings using matter. Staff are supposed to be looking into it.
So I’m not quite sure exactly how you were trying to do it, but there’s no way at the present time to get smartthings hub and its attached devices into Apple home except through homebridge. matter isn’t adding any functionality there.
More discussion in detail in the following thread:
Matter - smart home connectivity standard (formerly Project CHIP)