Pico battery connection and USB programming?

Ok, so you're using a separate charger module?

If so then everything is fine. Connect:

• The charger to the battery
  
• The battery to the Pico, via the 'Bat' pin (or a JST connector soldered on the bottom)
  
• Power the charger from the Pico's 5v pin
  
• Make sure the FET/B0 jumper is disconnected (it's only needed if you intend to charge the battery using the Pico, which isn't recommended!)
  
  

And I think that's it...