Apple's Technical Specifications for the Studio Display say that it is compatible with
So your Late 2014 Mac mini is not compatible with the Studio Display. A quick check of the Technical Specifications for that old Mini reveals why.
Mac mini (Late 2014) - Technical Specifications - Apple Support
The Late 2014 Mac mini has old-style Thunderbolt 2 ports, with Mini DisplayPort connectors, that have a top speed only half that of the Thunderbolt ports on the M2 Mac mini. It doesn't look like that Mini supports any Thunderbolt-attached display with a resolution higher than 2560x1600 pixels, or any HDMI-attached one with a resolution higher than 4096x2160 pixels.