In my experience the recover and save option does not work reliably.

Was there something else I was supposed to have done to copy the data across?
In hindsight ... back up your data to SD or USB or Extend_1, then format and recover.
As Extend_1 is a separate drive it makes sense to use it for (all) your own files.
As said previously, if you have not formatted, your data may well be there.
I am not clear ...
The suggestion to boot from SD Card
boot your system from a SD card
is different from using a recovery image on an SD card.
When you use the recovery image it is offering to recover the LLL to factory defaults, the save option is offering to try to save your data alongside the new operating system.
...
back to your first question,
whether anyone knew of any way to recover deleted files
Deleted files are moved to the hidden folder .trash.
Hidden filenames and foldernames all start with a . and can be found with your file manager, drop down the "View" menu, Check "Show Hidden Files".
Edit
I started to answer this question at a beginner level ... if it is pitched wrong, my humble apologies.
And welcome to the forum, Huskypete.

Cheers