This External Drive appears to be used as a Time Machine Backup Drive.
An External Drive used for for Time Machine Backup in Monterey macOS 12.5.1 is struck ( Rendered ) as a READ ONLY DRIVE and the user can not just Copy and Paste or for that matter Drag and Drop files onto it - period.
The above is by Apple Design and not an accident.
Empty Space - it is suggested to keep at least 15% to 20% of the Drive Total Capacity as Empty Space for good operations of the computer and for additional updates to Monterey to download, expand and install.
Rebuild the Spotlight index on your Mac
What is “Other” storage on a Mac, and how can I clean it out?
Free up storage space on your Mac
OmniDiskSweeper Safe to use
GrandPerspective
How to delete Time Machine snapshots on your Mac
See used and available storage space on your Mac
Locate backups of your iPhone, iPad, and iPod touch
Notation - If the user is using a cloning software like Carbon Copy Cloner - suggest tweaking the Safety Net Feature in this software. It may be making addition Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive
The final word from Apple on Managing the " Other/ System Data “ Category
Other / System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.
Suggestion - when posting images so not include the Serial Numbers of the computer as this is considered Identifiabel and Personal Information