larger boards are also more difficult to work with in general. JLCPCB plays a few tricks to keep the costs down on the smaller boards, but once you go past certain limits, the price goes up significantly.
Specifically JLCPCB claims "$0.0017 per joint" for PCB assembly, which would be around 10k joints for the transistors, and another 5k for the resistors, LEDs and other parts, so around $25 + the parts cost.
Some other PCB manufacturer (edit: PCBway) I checked also didn't seem to charge more than a few hundred per fully populated board (for the board + assembly).
It's of course possible that that JLCPCB pricing goes way up with such parts counts, but the other manufacturer did ask for count + size before producing the automatic quote.
Edit: Didn't realize you were the project author - thanks for the response! I guess that's what hides behind "Final price is subject to our review" then. Still, looking forward to seeing this in person