You can also hand-assemble surface mount parts by applying solder paste carefully to the pads, then placing all the components on the paste and heating the board until all the solder melts. That would have very time consuming for all those LEDs!
For a few hobby or toy things, the fixed rate board stuffing shops are the way to go.
Here is the link to the episode (without a timestamp): https://www.youtube.com/watch?v=S78lYvjo2JQ
And this is how the badges looked/worked: https://www.digikey.com/en/maker/tutorials/2025/assembling-y...
He did (there are centroid files in the production folder, which tell the board house where to put the components), but you'd be surprised at how possible it is to assemble something like this by hand. You won't believe me, but I find it easier than through-hole soldering (because you don't have to keep flipping the board over).
But there's a 99.9% chance this was done in-house at JLC or PCBWay.
*I haven't looked at the specific parts for this board, the LEDs look nice and could be a little pricey.
e.g.: