Lithium is the wrong chemistry for this novelty throwaway thing. Risks of fire all along the supply and disposal chain.
They could just use a few watch cells. LEDs use no power at all, so lithium not required; and watch cells aren’t hazardous when shorted.
Even the form factor of 18650 seems wrong for this, they would be so bulky compared to watch cells or AAA cells.
Watch cells are also usually lithium. I'd have just gone with LiFePO4 18650 cells.
That doesn’t solve the issue because the fire risk is due to short circuit. Any battery that is Li-based has too low IR to self limit.
Huh? A little CR2032 or similar cell has minimal short circuit current. A LiFePO4 18650 may not set itself on fire if shorted, but it could still set the rest of the badge or your shirt on fire.
The “badge” has a 2.8'' TFT screen, not just a couple of LEDs.