I connect my LG 4K display to my M1 MBA by HDMI via Apple's USB-C Digital AV Multiport Adaptor (which also gives me one USB-C for power and one USB-C for my wireless mouse dongle). This gives me 4K at 60Hz. I run the display at the middle scaling option (looks like 2560 x 1440), but all other scaling options are available to me. I can run the display at the native resolution, but it's too small for me. The 2560 x 1440 also gives true pixel doubling for a retina-like quality as at that setting, the MBA uses an internal resolution of 5K, then scales it down to 2560, which is exactly 2:1.
Most HDMI adaptors, and even USB-C to HDMI cables, will only support 4K at 30Hz, which is why I went with Apple's pricy adaptor (but then again, on a MBA, I needed the extra ports anyway). The MBA only has USB-C ports. Your Mac mini has HDMI, so use the cable that came with the monitor, or splash out on a nice expensive cable that can carry 60Hz.