macOS Time Machine is usually set up to work in the background and not overly affect anything that’s going on in the foreground while the user is working. Under normal circumstances, this is desirable behaviour. It is not desirable when you try to take one last backup of a failing SSD before it keels over completely. Which was the unfortunate situation I found myself in.
Turns out there is a sysctl that can be used to disable or enable this behaviour. If you turn it off, the backup in macOS Time Machine runs much faster, at the expense of additional network bandwidth and disk IOPS. The backup daemon will increase disk IOPS usage both for reading and writing.
The sysctl to turn off the low priority backup in the background is:
sudo sysctl debug.lowpri_throttle_enabled=0
Obviously, set the value back to its default of 1 if you want to restore the original behaviour. Based on the atop stats on my home server, network bandwidth usage went up from 5-10% to about 20%, and disk IOPS usage from 7-8% to about 65-70%. The backup is not maxing out the server or client. On my old 6 core Mac Pro, I have no problem running the backup at the higher speed without a big impact to my main work. I suspect that it would be different if I were to run disk intensive applications, though.