Glad it's working - although now I think you could safely remove that resistor if you wanted. Your first diagram was definitely correct.
All I can think is that your 4xAA wasn't outputting the 5.3v you thought... If you had 4 fresh AA then you'd expect 6v - and the Pico probably wouldn't be able to supply a high enough voltage for the data input of the LEDs (it tops out at 5v)... Also the LEDs are only meant for a 5.3v max input, so you could risk some damage to those as well.
NOTE: when developing - being connected to the IDE over USB - have Espruino's BatIn DISCONNECTED from you external 5V supply.
It should be fine to have BatIn connected to a battery while on USB with the Pico. It's different with the Espruino WiFi though as there's no BatIn pin.
Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
Glad it's working - although now I think you could safely remove that resistor if you wanted. Your first diagram was definitely correct.
All I can think is that your 4xAA wasn't outputting the 5.3v you thought... If you had 4 fresh AA then you'd expect 6v - and the Pico probably wouldn't be able to supply a high enough voltage for the data input of the LEDs (it tops out at 5v)... Also the LEDs are only meant for a 5.3v max input, so you could risk some damage to those as well.
It should be fine to have BatIn connected to a battery while on USB with the Pico. It's different with the Espruino WiFi though as there's no BatIn pin.