M4 Mini won't recognize 6k resolution monitor on Thunderbolt

Tto use ThunderBolt for a display, your cables should be clearly marked with the Thunderbolt logo, indicating they are certified. They also need to be shorter than 0.5 meters, unless you bought far more expensive (starts at US$125) ACTIVE thunderbolt cables.

¿Do your cables meet those requirements?

Both HDMI and DisplayPort (used inside Thunderbolt) are packet interfaces. In each case, the interface runs at one of a few Fixed speeds, and if there is LESS data than fully fills every packet at that speed, then packets are (generally) omitted.

HDMI data rates over USB-C (about 14.4 G bits/sec ) top out at 4K at 60 Hz for 8 bits/color of 4K at 50 Hz for 10 bits/color.

The HDMI standard says the next step up in speed takes 42 G bits/sec, which is higher than a Thunderbolt port can produce directly or with an adapter, if one were possible (40 G bits/sec for ThunderBolt display data). Apple was faced with a dilemma, and solved it by providing a DIRECT HDMI 2.1 port (for most M2 Macs and later) that runs as fast as about 42 G bits/sec.

That 42 G bits/sec HDMI 2.1 speed ALMOST supports your display at 10 bits/color using ULTRA cables (it needs 107 Percent) but with very slight modifications such as Display Stream Compression, it can be made to fit.

DisplayPort has slightly different quantum steps. DisplayPort data rates over USB-C (about 14.4 G bits/sec) top out at 4K at 81 Hz for 8 bits/color of 4K at 65 Hz for 10 bits/color.

The DisplayPort standard finally implemented says the next step up in speed, HBR3 under DisplyPort 1.4, takes 32.4 G bits/sec. There is an additional step that could have provided an increase to 40 G bits/sec, but due to the politics of the time, it was held off and the next big step was released as DisplayPort 2.0, which includes a new step up to UHBR10, which raises the data rate to 38.88 G bits sec.

Your display appears to only supports the lower DisplayPort 1.4 speed using DisplayPort direct or over Thunderbolt.

That 32.4 G bits/sec DisplayPort 1.4 speed supports a 5K display at 8 bits/color at 69 Hz, or a 5K display at 10 bits/color at 56 Hz.

If the display maker had chosen to support the higher UHBR10 at 38.88 G bits/sec, standard, that appears to support your 6K display at 8 bits/color, at about 70 Hz, and appears to support your 6K display at 10 bits/color at 60 Hz, but with NO margin of error (so it is possible it does not quite work).

Executive Summary:

That specific DISPLAY does not run that fast over DisplayPort direct or DisplayPort-over-Thunderbolt.

The Mini is working FINE.

What you are seeing is a limitation of the DISPLAY.

The Display-maker chose NOT to support a more modern version of DisplayPort, which limits the speeds the DISPLAY can attain using DisplayPort-over-ThunderBolt.

¿Works over HDMI ?

Then use HDMI !

you don't need/can't use Power Delivery, and can use a different hub for more USB ports.