MacBook Pro: Battery icon shows as charging even when not connected to power source
Welcome to AskDifferent! Try to perform a SMC reset, and possibly also a NVRAM reset.

From https://support.apple.com/en-us/HT201295: 


  The SMC is responsible for these and other low-level functions on Intel-based Mac computers:
  
  
  Responding to presses of the power button
  Responding to the display lid opening and closing on Mac notebooks
  Battery management
  Thermal management
  Sudden Motion Sensor (SMS)
  Ambient light sensing
  Keyboard backlighting
  Status indicator light (SIL) management
  Battery status indicator lights
  Selecting an external (instead of internal) video source for some iMac displays