  Advances in cosmic microwave background (CMB) science depend on increasing
the number of sensitive detectors observing the sky. New instruments deploy
large arrays of superconducting transition-edge sensor (TES) bolometers tiled
densely into ever larger focal planes. High multiplexing factors reduce the
thermal loading on the cryogenic receivers and simplify their design. We
present the design of focal-plane modules with an order of magnitude higher
multiplexing factor than has previously been achieved with TES bolometers. We
focus on the novel cold readout component, which employs microwave SQUID
multiplexing ($\mu$mux). Simons Observatory will use 49 modules containing
60,000 bolometers to make exquisitely sensitive measurements of the CMB. We
validate the focal-plane module design, presenting measurements of the readout
component with and without a prototype detector array of 1728
polarization-sensitive bolometers coupled to feedhorns. The readout component
achieves a $95\%$ yield and a 910 multiplexing factor. The median white noise
of each readout channel is 65 $\mathrm{pA/\sqrt{Hz}}$. This impacts the
projected SO mapping speed by $< 8\%$, which is less than is assumed in the
sensitivity projections. The results validate the full functionality of the
module. We discuss the measured performance in the context of SO science
requirements, which are exceeded.
