I tried the rolling release idea – by changing the repos – and doing the two-step upgrade that @Wayne suggested, but it didn’t go so well. I think @JJR’s “hesitancy” was probably well-founded 
In desperation over the many unmet dependencies I added bullseye main to the repo list, and the computer eventually booted up as a Debian machine, which was intriguing … 
So, I bit the bullet and did a complete backup of Home and then just re-installed a fresh install of byzantium – basically wiping the disc – and restored the files from Home into the new upgraded PureOS system.
This time I’m trying to stick to PureOS byzantium (and the Debian equivalent which is its basis) to the degree possible. So, repos are only byzantium (plus updates and security of course) and bullseye-backports, with the single exception of bullseye non-free so as to get the Bluetooth driver to work (per this discussion).
Pretty much everything has worked nicely, with the exception of getting my Epson printer to work again – which it did seamlessly in amber. Nothing has even remotely worked so far, so it is a continuing quest…