…you should change it back to “Battery” mode. “Wired” mode will indeed drain your battery quicker…solar panel or no solar panel.
You can go into the Device Settings/General Settings and then tap on Power Mode. It will probabably indicate that the camera is in Wired mode. Tap “Switch to Battery Mode” at the bottom. (You may or may not have to unplug your solar panel before you change back)
Fwiw, I sent my solar panel back for a refund. It just wasn’t effectively keeping my battery charged.