First, a whole lot of stuff starts happening when beginning with a new drive and a lot of tasks start running (more than normal) and depending on the amount of RAM that you have there could be memory swapping that could eventually go away. In addition, with starting anew, a lot of items need to be rebuilt and bookkeeping taking place. Note that kernel_task is responsible for memory swapping.
Also note, that Activity Monitor is the sum total of all reads and writes across all mounted drives and stuff can be read and re-written to them as part of macOS filesystem and Spotlight scans. It also resets after every reboot or shutdown and is only totaling use since the last reboot.
Also, check in ~/Library for any very large disk usage. If you have something like Daisy Disk, Omni Disk Sweeper, etc. it can make it easy to sort everything in order of size. Something may have gone ballistic and started writing massive amounts of data to caches or other databases. You may also have encountered a Spotlight going berserk issue that has been seen occasionally (happened to me once).
Something I use to track individual disk is a command line app called smartctl although you can get commercial GUI based apps that can do the same thing like DriveDx. Since the drive is a Thunderbolt drive these can access that info directly without any special USB driver (the USB MSC class has no direct way to read SMART data).
I would suggest getting one of those apps if you did not find any out of line data in ~/Library, establish a base line and then check perhaps daily and see how much the writes change.