I wouldn't think that the 2500x1600 resolution or 16:10 aspect ratio would be a problem. Apple came out with a 30" Cinema Display with that same resolution more than 20 years ago, and many people have attached 24" 1920x1200 pixel monitors to Macs over the years.
Whether the M4 Mac mini will power the monitor might be a different question. USB-C allows for the negotiation of Power Delivery in either direction, but as far as I know, Apple's Technical Specifications do not promise the delivery of large amounts of power to external devices – and there have been reports of portable monitors not being able to get (enough) power from MacBook Pros containing M4-series chips.
Assuming that this is the monitor in question:
https://www.arzopa.com/products/arzopa-z1rc-2k-portable-monitor-brilliant-qhd-500nits-8bit-display
the monitor manufacturer themselves raises the possibility that you will need to give the monitor its own separate USB-C power supply.
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"This portable monitor does not contain any battery. If the monitor appears to flicker or restart when adjusting the brightness or others, please check whether the power supply is sufficient for the monitor. It is recommended to use the power adapter that supports 5V/3A or above for power supply."
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