I haven't seen "my" answer to this problem so I am posting both Q & A here.
I am doing initial WiFi backup of 265GB on a 16" MacBook Pro, running system 10.15.1, to a 2TB Time Capsule. I have done full backups many times before: they have been slow, but not like this. Today's backup includes long stretches of no network activity, punctuated by brief – but small — bursts.
The progress bar declines to offer a prediction, but my estimate is about a week.
I have rebooted, erased the Time Capsule (via AirPort Utility, not Disk Utility) twice and re-started. Apps like Music and Photos were closed anyway. Tried the throttle hack (https://www.imore.com/how-speed-your-time-machine-backups). Pored through dozens of outdated suggestions online.
What finally got it rolling? Answer to follow.
Best Answer
After about six hours of waiting for Godot, I tried this experiment: put the Mac to sleep (power not connected) and see if (still sloooow) backup proceeds while sleeping. It did not. (I let it sleep for a half hour, so the presence or absence of progress would be more apparent.) But... on re-awakening, the backup was more than 10x faster.
Also, I found that when power is connected, backup does continue while sleeping. (PowerNap feature, checkbox in System Preferences > Energy Saver panel.) So while both laptop and I were asleep, 90% of the backup completed.
Solution? I don't know how general it is, and this is post-hoc reasoning, but my suggestion is: try putting your Mac to sleep for a while, with power disconnected. On awakening, it might just be 10x faster.