the Mac Studio Display requires a DIRECT ThunderBolt connection, or a setup that provide the equivalent Thunderbolt connection over appropriately short cables The typical cable length allowed between Hubs or Devices at these data rates is 0.5 meters or less for each length of cable.
You can extend the individual cable lengths by using ACTIVE ThunderBolt cables, which have drivers in the cable. These typically convert to Fiber Optic for the length of the cable, then back to electronic signaling at the far end. Costs are typically over US$150 per cable.
If you are NOT doing Full-motion Video or equivalent, there are several way to make a connection with lower data demands. But these may not be the solution you were looking for either.
Continuity, including Airplay, is the first that comes to mind. but remember you will be using your Wi-Fi network for most of this data, and that may be overwhelming AND you don't get two devices using this method, because it requires the video data compressor/decompressor Hardware to be fully involved in squeezing the data down to fit over a narrow Wi-Fi 'pipe', then puffing it up again at the receiving end.
Screen sharing is another feature that can be used to share your main screen into a window on a different Mac. this uses your network as well, but if you have a faster ethernet connection, this feature can be more responsive and less taxing than just using Wi-Fi.
[In my opinion] you would be FAR better served by using none of this and just buying an additional display for the Mini.