Backdrop community pay a lot of attention to UX issues. And it is priceless. As a result Backdrop is several steps ahead of Drupal (and many other CMS) in terms of UX.
I would like to propose new UI button group component for Backdrop. It is select component which act like radio buttons or checkboxes. You could see it many times before all over the internet. It is present in bootstrap css/js framework.

It is perfect solution when you have just few options to choose. Its main advantage that you can see all options immediately without additional clicking. Button group needs one click less than selectbox to provide action.
Here's how it might look on Manage content page. Both options are chosen. It is analog of "- Any -" option.

Here's one option chosen.

Manage user accounts page.

This component can be used widely. It is just a sketch. Styles needs to be discussed.
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