Yes, once SmartThings has released full Matter support. The hub has been certified, but that doesn’t mean you can use it with matter yet. The backend platform still needs to be completed, each individual hub needs to be updated, and there needs to be an update to the app.
- What about Zigbee or Z-Wave Matter devices (if there is such a thing).
There aren’t any planned yet. There are a number of Zigbee devices which will connect to Matter-certified hubs/bridges and that bridge can bring them into matter if the bridge also has a Wi-Fi/ethernet connection. For example, the Philips hue hub will do this.
- What is a “Matter bridge” and what does it mean that this won’t happen soon?
A “matter bridge” is one of those devices like the Hue hub that we just mentioned that will be able to expose some of the devices connected to it to matter. So that’s one way integration out.
A “matter controller” provides one-way integration in. It allows you to add Matter compatible devices, including Matter Bridges, to your setup as well as standalone matter devices. So it can communicate to those matter devices,
The Smartthings/Aeotec will be a matter controller. It will be able to communicate to your individual matter compatible light switches and sensors and other devices and you will be able to add Matter Bridges as well as those individual devices to the smartthings app.
The smartthings/Aeotec hub will not be a Matter bridge, So you will not be able to add it to, for example, the Apple Home app or the Ikea Dirigera app.
- Can I control both Matter and existing devices from the Smarttings app? Can I use Sharptools to write rules that say, “if a Matter sensor does X then do Y with my existing Z-wave switch?”
Yes. That’s the good news. 
- Suppose I add Matter devices that communicate with Thread. Do I need a Thread border router for these to work. Where do I get one? Once I add this, can I control all of those through the Smartthings app? Can I write Sharptools rules around them all?
Yes, you need one thread border router in your house. That will talk to all your Matter-compatible thread devices and it will probably have a Wi-Fi/ethernet connection to get to your matter controller. That’s how it will work with smartthings if you don’t have a smartthings hub, for example. Or if you only have a V2 hub.
Amazon is going to update many of its echo devices to be thread border routers, and Google home is going to do the same with some of its, and an Apple HomePod mini is also a Thread board or router, so most people will have a voice assistant that can perform this role.
- What is different with the v3 hub? If I wanted to upgrade to the v3 hub, what would that entail?
Others have given you the technical details on the differences. We should say that there isn’t really an upgrade or migration process between one smartthings hub and another regardless of the generation. You just have to completely rebuild your network on the new hub. Which is a pain. There was briefly a migration tool that support could use between two V3 hubs, but it seems to have been discontinued because it didn’t work all that well.
You can read more about Matter in the following discussion thread: