Drupal 8 includes a "Migrate UI" module helps people upgrade from Drupal 7 to Drupal 8. I'd like to see something similar for Backdrop that will help people move from Drupal 7.
The Drupal 8 also provides data on available upgrade paths (similar to what we can provide with https://github.com/backdrop-contrib/backdrop_upgrade_status) as well as an interface for uploading both files and database from an existing Drupal 7 site, into the current Backdrop site.
The first page of the upgrade process contains instructions:

The second page asks for your Drupal 7 database and Drupal 7 files:

The third page does an analysis of the modules you've installed on the new/empty (Backdrop) site and what's in the old legacy database, and generates a report:

If the new new/empty (Backdrop) site has content it it, it throws a warning first:

I would like to start working on this as a contrib module, but am interested to see what other people think about having something like this in core.
Recent comments
Thanks, the /tmp folder was the problem. I moved it elsewhere and then the updated worked. Thanks again!
Update 1.35.1 appears to install but hasn't
Probably not the reason, but worth to do a quick check: Sometimes the update cache interferes, so if something's odd with updates - some module (or core) claims to have updated, but then...
Update 1.35.1 appears to install but hasn't
Nope, not touched any permissions!
Update 1.35.1 appears to install but hasn't