I know for the original charger with the shorter cable people made 3d printable holders for it to fit more snugly, but I don’t know if those would work for the OLED charger with its longer cord.
You might need to get a third party case with an internal storage compartment - eg the jsaux case.
The color might be a form of HDR visualization if you’ve got an OLED Deck. Try turning that setting off from the Deck’s display menu if you do.