Battery is always charging even I only use it in wired mode.
This should only happen when you re-power the keyboard. Lithium battery power is not used when plugging in USB but it would also drop slightly when not in use due to self-discharge.
Self-discharge of batteries is a normal chemical phenomenon, which refers to internal chemical reactions reducing the battery’s stored charge without any connection between the electrodes or any external circuit.
Self-discharge is a chemical reaction, just as closed-circuit discharge is, and tends to occur more quickly at higher temperatures. Storing batteries at lower temperatures thus reduces the rate of self-discharge and preserves the initial energy stored in the battery. Self-discharge is also thought to be reduced as a passivation layer develops on the electrodes over time.