Bismark There's an experimental desktop mode but it requires developer options to enable desktop mode + freeform window mode on secondary display. It doesn't have a lot of features yet. It will be available outside developer options by Android when it's actually ready for regular users to use it, maybe with Android 16 or one of the Android 16 quarterly releases.
Bismark There are USB-C hubs with passthrough for DisplayPort alternate mode, and if that is done via USB-C then you could use the cable you already bought. Some hubs may include other video outputs, etc.