Frozen recovery screen on Mac mini with M4 chip after HD erase

Disconnect all unnecessary external devices including any that are connected to the display.

More than likely you will need to perform a DFU Firmware Revive which resets the security enclave chip & system firmware. If this still does not solve the problem, then you will need to go with the last & most drastic option of a DFU Firmware Restore which does the same thing as the "Revive" except it also resets the internal SSD resulting in the internal SSD being erased as well as pushing a clean copy of macOS onto the internal SSD. Unfortunately the DFU Firmware Revive and Restore process requires access to another Mac (most likely running macOS 15.x Sequoia).

How to revive or restore Mac firmware - Apple Support

If none of this helps, then you most likely have a hardware issue of some sort (most likely a Logic Board failure) that will require a hardware repair.

I hope you have a good backup of the data on the internal SSD because you won't be able to access the data unless one of the first two suggestions fixes the problem since the last two suggestions (Firmware Restore & hardware repair) will result in the loss of data.