LiPo LED/Fiber job not working correctly after plugged in
Your description isn't clear, but given the basics of the charger and 2 batteries, and usb source, the problem is clear. You aren't using the right setup. Your charger is for a single 3.7V LIPO, A 1S charger. You have 2 batteries in series, 2S, and 5V is not enough to charge a set of batteries that have a 6.4 to 8.4 voltage range. The batteries have a protection circuit, they are likely going into ULVP mode, or ultra low voltage protection mode so it doesn't work until they start getting charged up to the right voltage (by &quot;jumping it&quot;).
The 5V or less output from the charger when connected to USB would power some of the led sections, but obviously cannot fully power 2x 3.2V white leds in series. The 2x red leds will light up fairly bright, and the 1x white would, the 3x red will be dim, but the 2x white and 2x red + 1x white would not, if at all.
Solution, replace the two batteries with a single lipo AND replace all the led branches that won't work directly off the single lipo. OR replace the charger board with a 2S controller (like this, no personal experience https://www.mouser.com/new/dfrobot/dfrobot-dfr0564-usb-charger/ which has a built in boost circuit from usb 5V), and you may still want to double check the led resistor values based of the real voltage range of 7 to 8.4.