Soft gripper robots provide superior safety, adaptability, and compliance compared to rigid robots. However, soft grippers must address inadequate stiffness and interference resistance. Soft pneumatic electroadhesion (EA) grippers with variable stiffness are potential options for addressing these difficulties. In this paper, we present a soft bionic gripper (SOBG) that resembles human finger movements, such as bending and deflection, employing pneumatic actuation, and whose stiffness is effectively decoupled from its position through a layer jamming-induced variable stiffness structure. By applying electroadhesive forces, the SOBG can perform complex motion tasks that would typically require a wrist joint, making them simpler to perform than with conventional flexible grippers. In addition, the SOBG can perform one-finger object manipulation to grasp flat, concave, and convex objects. To show the potential for more complex robotic applications, we evaluated each function independently by presenting a demonstration of cap-screwing, a material handling system, and an anti-interference research. The SOBG concept and solution proposed in this study may pave the way for the easy integration of EA into soft robotic systems and promote the wider use of EA technology.