The original LEDs are just wired together. The link says the power source is "Universal USB wall
charger or 3X AA Batteries". Based on that description, the LEDs would seem to be wired in parallel.

It would seem the that 5mm LEDs you linked to, would be huge compared to those of the original.
A smaller alternative would be these https://www.adafruit.com/product/5491
https://www.amazon.com/ZZHOB-25PCS-Pre-Wired-0805-Light/dp/B09MWGRRTP

If you want them individually addressable, here is a chip for a PCB. 10 chips = 30 LEDs.
ws2811 driver 10 pack https://www.adafruit.com/product/1378
Each chip has 3 drive outputs, so you could use 3 single color LEDs instead of an RGB LED.

To make it compatible with WLED, you need to drive this with ESP8266 or ESP32.

Not directly related, but here is a 'weird' Address LED version.
Fixed Address NeoPixel LED Fairy Lights - 100 Wired LEDs
https://www.adafruit.com/product/4917