Best cable to connect M4 Mac Mini, which has a thunderbolt 4 port to Apple Studio Display, which has a thunderbolt 3 port.

There is no difference between my M1 Mac Mini (TB3) or M4 Mac Mini (TB4) when connecting to Studio Display (equipped with TB3); no matter TB3 or TB4 cables I was using.

I have not seen any cable with "TB3 at one end" and "TB4 at the other". If any doubt, choose TB4 cable --> it is backward compatible with TB3.

Best

There should be nothing wrong with using the Thunderbolt cable that comes in the monitor box.

If you are tempted to use another cable, make sure that it is a genuine Thunderbolt 3 or Thunderbolt 4 cable that is no longer than 1 meter (~3 feet). Current versions of macOS do not like to see display transmission errors and may cut resolution or signal if they see them. Using long cables increases the chance of such errors.

I have tested TB3, TB4 and TB5 cables with the Studio display and no difference using my Mac Mini M4.