Sometimes you will need user interaction to perform certain updates. For example, Backdrop 1.4.0 has a new installer module, but you need to manually look for it and enable it, which causes confusion to users expecting to have all new features after an update.
This could be handled in different ways, like enabling new features on updates, but "power users" will not be happy about this.
Another way is to ask the user if he wants "Pretty new feature" in the update process, like this:

The update script is however very basic, so forms won't be validated in any way, but you could use these forms to pass user input to update scripts.
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