Change Background Color of Side Pane on Kate
This Tip shows you How to Change the Side Panel Background Color on Kate Editor – Step by step Tutorial.
And this solution is very easy because Kate dispose of a wide range of Color Themes for the Panels.
Especially relevant: this solution may Works only on a KDE Plasma 5 like desktop.

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Changing Color
Simply Navigate to Settings >> Color Theme on the Top Menu Bar
Like in the pic here below: