What files were backed up and how?

the entire hard disk was back up to my external hard drive ... that’s as much as I know ... everything else came through fine except for Firefox ... with Safari for example : all the Favourites, Bookmarks and the entire Reading List cam across ...

So the files and folders were copied?

I don't know what your profile looks like at the moment, so;

First: Use these links to create a new profile. Use this new profile as is.

https://support.mozilla.org/en-US/kb/how-run-firefox-when-profile-missing-inaccessible

http://kb.mozillazine.org/Profile_folder_-_Firefox#Navigating_to_the_profile_folder

https://support.mozilla.org/en-US/kb/profile-manager-create-and-remove-firefox-profiles

https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

Type about:profiles<enter> in the address bar.

Next: When you are ready, we can start moving parts of your old data and Copy it to the new profile.

First; open your file browser to the New profile;

Type about:support<enter> in the address bar.

Under the page logo on the left side, you will see Application Basics. Under this find Profile Folder. To its right press the button Show Folder. This will open your file browser to the current Firefox profile. Now Close Firefox.

Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder

Linux: Under the page logo on the left side, you will see Application Basics. Under this find Profile Directory. To its right press the button Open Directory.

Second, open another file browser to the Old profile on the backup.

Warning ! ! Only Copy the files you are told. We will avoid anything that might cause problems. Here is the list of files;

cookies: cookies.sqlite Do not bother. Cookies will be created when you return to the website. However, you will have to log in everywhere. And you may lose any settings that websites store on your computer.

extensions(add-ons, themes): it would be better to download them fresh. If you need to remember what add-ons you had, open the extensions sub-folder and look at the .xpi files

logins.json and key3.db [v58+]key4.db : These are the password files. Copy Both !

persdict.dat : custom dictionary - words you added to the dictionary

mimeTypes.rdf [v55+]handlers.json : What to do with what type of file.

places.sqlite : History and Bookmarks.

prefs.js : Your settings. Note: If you were having problems, this could be contaminated.

cert8.db [v58+]cert9.db and possibly cert_override.txt : Stores all your security certificate settings and any SSL certificates you have imported into Firefox. If removed, the cert8.db, cert9.db file will be replaced.

search.json.mozlz4 : file stores the user-installed search engines that are available in the Firefox v47+

search.sqlite file and searchplugins folder store the search engines that are available in the Firefox Search bar before Firefox v47

Copy these files from the old to the new. You may get a message that the files already exist. Choose to over-write for each file.

Many thanks for this FredMcD‼️ As a result of other issues I had to reset my MacBook to an earlier operating system [MacOS Catalina] which partly resolved the problem of lost Bookmarks ... but the Reading List was not restored and I had many valuable «reads» saved there ... is there a straightforward way of finding and reinstating the Reading List? I thank you warmly in advance for any insights

Sorry, I don't know Mac's.