Update: Seems there is a bigger issue. The original problem I was trying to solve was strange volume error messages. Did a macOS reinstall, hoping that would go away. It didn't. Later, started to see occasional kernel panics.
Decided to erase the volume, and start over. That's how I ended up down the path of trying to reinstall, but painted myself into a corner with the T2 chip and disabled booting from an external drive. (Hint: enable booting from external media before you wipe the drive, or you'll be stuck). Then there was some mystery issue with the local network causing the Internet Restore loading of macOS to fail. Tried it on a different network, and made some progress.
Then I ran into "The operation couldn't be completed. Permission denied" when it was attempting to install macOS. The installer log showed:
Could not create mutable product at /Volumes/Macintosh HD/macOS Install Data (error 28).
- [OSISHelperProxy createMutableProductAtMountPoint: J_block_invoke_2: Error Domain-NSPOSIXErrorDomain Code-28 "No space left on device" etupd (641):
- [OSISCreateMutable roductOperation startWithDelegate:]: Could not create mutable product at mount point: /Volumes/Macintosh HD etupd (641) : Operation queue failed with error: Error Domain-NSPOSIXErrorDomain Code 13 "Permission denied"
Stopped operation queue with Error Domain-NSPOSIXErrorDomain Code 13 "Permission denied"
To me, it was starting to look like an SSD issue.
Took it to the Genius Bar today, they did a diagnostic, but the SSD passed. They recommended a main logic board replacement, primarily due to the kernel panics. Covered under AppleCare+. We'll see what happens.
Thanks to all who replied.