Hm, I'm unable to reproduce this on the 1.x branch... but pushing my PR anyway. Perhaps it will help someone else.

I haven't tested it, but I believe @jenlampton's PR would prevent the notices appearing. However, it doesn't fix the root problem, which is that feeds_get_plugins() (which is where $plugin['module'] comes from) doesn't actually have a module key at all...

Here's one of the array keys returned by feeds_get_plugins():

FeedsNodeProcessor (Array, 4 elements)
  name (String, 14 characters ) Node processor
  description (String, 24 characters ) Create and update nodes.
  help (String, 44 characters ) Create and update nodes from parsed content.
  handler (Array, 4 elements)
    parent (String, 14 characters ) FeedsProcessor
    class (String, 18 characters ) FeedsNodeProcessor
    file (String, 22 characters ) FeedsNodeProcessor.inc
    path (String, 37 characters ) ./modules/feeds/plugins

No module key...

So I think this issue needs some more work (by someone who knows more about how Feeds should work than I do).

@BWPanda Drupal 7 uses ctools_get_plugins() function instead of feeds_get_plugins() here, and that function provides module keys, but that function is not implemented in Backdrop.
(I encountered this bug when converting the ldap_feeds module.)

Here's some docs on converting feeds plugins for Backdrop:
https://github.com/backdrop-contrib/ctools/wiki/Converting-CTools-plugins

It looks like maybe all that is needed is adding a module key to the plugins? I bet ctools did that automatically, but we can do it explicitly.

I just ran into this again. It happened immediately when I first installed feeds module.

I've filed a new PR that adds the missing module key to all feeds plugins in this module: #13

I'm getting flooded with these errors, which I assume is the same problem - just different line number.

Notice: Undefined index: module in feeds_system_info_alter() (line 896 of backdrop/modules/contrib/feeds/feeds.module)

@stpaultim have you tested the PR? I just applied that to a new site and it resolved the issue for me.

@jenlampton I just replaced the feeds module with your branch and I'm no longer flooded with errors, but I am getting a single error.

Notice: Undefined index: module in feeds_system_info_alter() (line 896 of /var/www/triplo/all-modules/simplo/src/modules/contrib/feeds/feeds.module).

I will try to do a little more testing later tonight.