MS510TX, can't manage because "not in the same subnet"

One would expect the MS510TX would be able to receive a DHCP assigned IP address, e.g. from your ASUS XT8 Mesh primary node if it's in router mode. Ensure the MS510TX MAC address is added to any security on this router, so it can get access to the network like any other wired or wireless device.

The alternate approach would be to temporarily configure a computer into that other 192.168.0.x/24 network, like 192.168.0.123, MAsk 255.255.255.0, default gateway and DNS 192.168.0.1 (regardless if it exists, and override any kind of connectivity tests. Now you can ping the switch on 192.168.0.239, access the management Web interface using a Web browser, set a fixed IP (not overlapping, ideally outside of the routers DHCP pool) in your LAN subnet (like 192.168.1.123, mask 255.255.255.0, gateway 192.168.1.1, DNS 192.168.1.1). From here ou should be able to reach the switch from your nomal LAN/WLAN network (driven by the Asus router!). Everything under the assumption the Asus does isue 192.168.1.x addresses of course.