Home Assistant
Matter controller: yes. “meaning that it can control Matter-based devices” — home-assistant.io
Matter version: 1.6. “Supports Matter 1.6.0” — github.com
Zigbee radio: Home Assistant Yellow (built-in Zigbee radio), Connect ZBT-2 USB (recommended for new networks), Connect ZBT-1 USB (discontinued, still supported). “Home Assistant Green does not have a built-in Zigbee radio.” — home-assistant.io
Z-Wave radio: Home Assistant Connect ZWA-2 (Z-Wave and Z-Wave Long Range, 800-series, MSRP $69). “Run both your Z-Wave and Z-Wave Long Range networks simultaneously” — home-assistant.io
Matter device types: 9 listed, 1 not listed or partial
Listed: light, lock, cover, climate, switch, sensor, update, vacuum, bridges (bridged devices appear as devices). “Light, Lock, Cover, Climate, Switch, Sensor, Update, and Vacuum” — home-assistant.io
Not listed or partial: cameras, doorbells, closures: server supports 1.5.1 but frontend support still being built.
Needs the official Matter Server app on Home Assistant OS (not on 32-bit systems). It accepts the Thread border routers of other ecosystems (Nest Hub 2nd gen, Nest Wifi Pro, HomePod mini or 2nd gen, Apple TV 4K) or its own OpenThread Border Router app on a Connect ZBT-1, ZBT-2 or SkyConnect. Home Assistant Green ($199) has no radio of its own (home-assistant.io); a Connect ZBT-2 ($49) runs Zigbee or Thread, not both at once (home-assistant.io).