Boards, but can you get the pick and place and the soldering done? I wouldn't want to be soldering that many LEDs by hand!

Every major chinese PCB supplier has offered very affordable PCB assembly ("PCBA") for several years now where you give the gerbers for the boards along with a BOM with part numbers from a mutual supplier catalog and p'np / solderpaste mask data and they will load up a p'np machine and oven run a small batch of boards for you.

e.g.:

https://jlcpcb.com/smt-assembly

https://www.pcbway.com/pcb-assembly.html

That price is including PCBA. Without it would be <$1/board