Allan Jones was correct!
I disconnected the two (physically small) SSDs which were also connected by USB and lo and behold, when I reconnected it, the DVD drive was accessible -- for about 15 seconds! It is obviously a USB-power problem and I have now ordered a powered hub.
Nothing else has changed -- other than the version of OS X -- since last time the DVD writer worked (without problems), so I'm wondering if "Catalina" puts additional requirements on the power supply? (Although why it would affect the USB power is beyond my comprehension capacity!)
Given that I will want to keep up to date with OS X (or whatever comes after it!), I shall probably invest in a Mac Mini and use my Intel-powered iMac as a 21" display! (Last time I did not keep to the latest OS version, my iPhoto library became "damaged" -- how, I have no idea! -- and I still have not recovered from that, with Photo having 'lost' the library on the iMac and 5 partial-libraries [thanks to a repair/recovery utility which no longer works!] for iPhoto, none of which is currently accessible. Luckily, I have more recent photos on iPad and iPhone, but have lost all -- several hundred -- pre-2014 photos.)
Thanks for reading my tale of woe and thanks to Allan Jones for putting me on the right track regarding the USB power problem.