How does one change the amount of time the notifications popup thing stays visible?

At this time this setting does not exist. Note that unless the notification itself is destroyed automatically ( many aren't ) simply clicking on the notification icon in the tray will show them again, until it is clicked again.

Ok. I look forward to seeing this feature implemented in future releases. Thank you.

Note that developers cannot consider your idea unless a wish exists in the KDE Bugzilla. ( https://bugs.kde.org )