Yes! That seems to have (mostly) worked: I now have 'user-data' copied off my broken phone and onto my laptop. Thank you everyone for your help.
Now the bad news:- Pushing the data onto my replacement phone did not work very well.
I bought a replacement Pixel 3a of the same spec. Down grading to Android version 9 was a bit of a struggle as the Android Flash Tool kept failing repeatedly due to a 'Network Error' while downloading the new image. I eventually got it too work by swapping to a computer that had an ethernet connection to my router, rather than using wi-fi, and that worked first time. Installation of Touch (version 20.04) worked well, the only small problem being that the phone was not automatically recognised when I first started the installer. I was also able to push the 'user-data' from my laptop onto my newly set-up replacement phone, but this broke several of the installed applications! Gallery and Music would not open at all, and Messages was so corrupted that I could not read the texts. The only good result was that Contacts worked and I have been able to export a copy to my laptop.
I understand that there is quite a big difference between the operating systems on Xenial and Focal, so I can only assume that there is also a difference in the contents of the hidden config files in the 'user-data' folder between a phone that has been upgraded compared with a phone that is a fresh install. And that it is these differences that have caused certain apps to fail.
I have reinstalled Focal on the new phone, and wiped the user data. I now have a phone that works as expected. I shall copy photos, music, and contacts over using the standard MTP service. I will also have to accept that the old text messages are lost. I am content with this; a 95% recovery of data from a broken phone is a good result. Thank you all again.