Time Capsule/Time Machine volume slow to process with tmutil
I don’t think anything is wrong. The hard link directory nature of a time machine backup is extraordinarily iops constrained and coupled with the limited power of the disk controller in AirPort, you’re far better off copying off the files you want to keep and then erasing the volume. 

Each backup has a directory entry for each and every file present on the source so each backup interval deletion is actually a ton of work (whereby a ton is defined as 250,000 directory entries with ACL, permissions, date metadata, etc...)

Your network measures are spot on, and I worry your TimeCapsule drive could be failing if a simple ls is lagging so badly.