I was unable to install updates for several months, roughly August to November 2023. I finally diagnosed and fixed the problem. Just in case this works for someone else, I thought I would record my process here.
Some time after updates stopped working, I opened Device Manager and discovered that it was uncontrollably refreshing itself every ~2 seconds. Eventually, I looked into solutions for that. Most of the info I found said that the likely culprit was a bad USB device. But I unplugged all of my USB devices and the problem persisted.
A little while later, I noticed that all Bluetooth information and controls had disappeared from "Settings > Bluetooth & devices". I don't use Bluetooth routinely, so I hadn't immediately been aware that Bluetooth had stopped working.
Then it occurred to me that if the Bluetooth driver was causing the Device Manager refresh loop, it might also be interfering with Windows Update. So with some difficulty I managed to right-click on the Bluetooth device in Device Manager while it was visible between refreshes, and disabled the device. No luck. So I deleted the driver, and Device Manager stopped refreshing! Even better, Windows Update worked smooth as glass.
I decided I wanted Bluetooth available if I needed it, so I went to the vendor site, downloaded and installed the latest driver, and rebooted the system. Device Manager was stable, Windows Update continued to work, and Bluetooth now also worked as well.
So my advice is that if Windows Update is failing and other solutions don't work, open Device Manager and see if it's in a refresh loop. If it is, the underlying problem is probably a bad device. Try unplugging USB devices first, and if that doesn't work, start poking around and looking for other symptoms that might supply clues pointing to the culprit device.