I started tweaking #4020 and quickly got into multiple interesting rabbit holes ...in the end I got a very nice result, but there were multiple changes in all sorts of places, and I'm afraid that a single PR would make this unreviewable. So I'm filing this as a meta issue, to get all the bits implemented incrementally.
Here's what I have so far (admin user - CSS still needs some work):

Changes:
- [ ] Zebra stripping the rows in the block, for better scannability.
- [ ] Tweaked
theme_more_link()to allow custom "more" link text/properties, and made that "All recent content" for this block. - [ ] Made the "Number of recent content items to display" field in the block settings a number field instead of a select with limited options.
- [ ] Make the edit/delete links dropbuttons instead.
- [ ] Adjust the colspan of the content/author column cells, depending on whether the operations buttons are shown or not for each row (based on permissions the current user has).
- [ ] Add checkbox in the block settings, to show the operations dropbuttons column or not.
- [ ] Proper "submitted by" info, pulled from the content type settings, instead of just the author username
- [ ] Add checkbox in the block settings, to show the "submitted by" info or not.
- [ ] Render the username link via a new [node:author:link] token (see https://www.drupal.org/project/token/issues/1176592 and https://www.drupal.org/project/token/issues/698242)
- [ ] Moved
sevenDropButtonWidths()that helps calculate dropbutton widths fromcore/themes/seven/js/script.jstocore/misc/dropbutton.js(and renamed it todropButtonWidths()), so it can be used in Basis and other themes.
Happy to discuss each of these changes and either do or not.
Here's a few more screenshots...
anonymous user viewing the page ("submitted by" info hidden):

another_userlogged in ("Editor" role, author of the second piece of content in the table - has no permission to delete own content):
block settings dialog:

Recent comments
UPDATE: I fixed the errors that I found in the logs. They were related to deleting an old blog content type pulled over from Drupal that was still referenced in one of the layouts. I updated...
missing "add block" in custom layout
Hmmm... this sounds like a bug with Copy Blocks. Would this possibly be related: https://github.com/backdrop-contrib/copy_blocks/issues/26 https://github.com/backdrop-contrib/...
missing "add block" in custom layout
Also this error: Warning: Undefined array key "blog" in summary() (line 63 of /app/core/modules/layout/plugins/access/entity_bundle_layout_access.inc). I did recently delete an old blog...
missing "add block" in custom layout