Thank you again for the Report.
Have picked out Only items from the Report I believe are important to this issue of Improper Shutdown message
Q - Clean up - There are orphan files that could be removed.
A - Self explanatory
Q - Unsigned files - There are unsigned software files installed. These files could be old, incompatible, and cause problems. They should be reviewed.
A - Also Self explanatory and with checking Third Part Software, extensions and Drivers are Monterey Compatible
Q - System modifications - There are a large number of system modifications running in the background.
A - Running large number of system modifications can occur by User purposeful actions and / or by Third Party Installed and used on the computer.
A - This conditions tends to make the System (computer ) less reliable and can led to unintended consequence such s what is happening now.
Hardware Information:
Q - Mac mini (Late 2014)
Mac mini Model: Macmini7,1
A - Niece machine and have 1 from 2011. But I know it will eventual need to be replaced even after Replacing the Fusion Drive with a 500 GB SSD Drive and upgrading to Max RAM
Drives:
Q - disk0 - APPLE SSD SM0128G 121.33 GB (Solid State - TRIM: Yes)
disk0 - APPLE SSD SM0128G 121.33 GB (Solid State - TRIM: Yes)
Internal PCI 5.0 GT/s x2 Serial ATA
disk0s1 - EFI (MS-DOS FAT32) [EFI] 210 MB
disk0s2 [APFS Fusion Drive] 121.12 GB
disk1 - APPLE HDD HTS541010A9E662 1.00 TB (Mechanical - 5400 RPM)
A - Fusion Drive are good for extra Storage but will receive a major Decrease in Performance in basically Big Sur macOS 11 and above
A - The Newer versions of macOS 11, 12, 13 are all basically designed by Apple to run on a ALL SSD Drive >> IMHO
Q - External USB 5 Gbit/s USB
disk4 - SAMSUNG HD501LJ 500.11 GB
Q - External USB 480 Mbit/s USB
A - The Improper Shutdown message maybe related to either of the two External Drives.
A - Suggest try running the machine and properly Dismounting both Drive Before shutting down and see if the issue presents what going a Restart.