What is the equivalent for zigbee2mqtt for Matter/Threads?
You can probably plumb Home Assistant into your MQTT server from there.
That is I don't want google/amazon/samsung/apple to control my house. Most border routers are also connect to our smart home system. (there are exceptions but it isn't clear if they are better)
For what you're looking to do in principle you don't really need any of this after the initial commissioning. So long as the radio waves can reach the devices they will be able to talk to each other.
Their latest one has two radios so you can do both Zigbee and Thread from a single device.
I've found however, that Thread prefers several border routers around my house to operate well.