Hi,
If the components are all in the JLCPCB assembly catalogue, JLCPCB will assemble it cheaper than anyone else. It looks like most of the parts are not super tiny.
If the components aren't all in stock (do they have the nrf modules?) then it is difficult and possibly expensive to get JLC to procure them, you're probably better (in my experience) going with someone else who does a more "manual" system. The other companies charge more upfront fixed cost ("Engineering fee" or whatever) than JLC, as they're less automated, but have a higher degree of flexibility, as they will go and buy just the quantity required of the components (Maybe + a small amount of wastage)
My experience has been with JLCPCB, PCBWay and ospcb (cnospcb). PCBWay gave the best feedback and support, but unfortunately seem to have made some mistakes on a couple of my boards (although the rest of the batch seem ok)
Looking at the design, it looks like there is a surface mount battery holder on the back. If you're willing to solder those on yourself, then you'll find it's easier to get the rest assembled as it won't require a 2-sided process.
Mark