  We report ALMA observations with resolution $\approx0.5$" at 3 mm of the
extended Sgr B2 cloud in the Central Molecular Zone (CMZ). We detect 271
compact sources, most of which are smaller than 5000 AU. By ruling out
alternative possibilities, we conclude that these sources consist of a mix of
hypercompact HII regions and young stellar objects (YSOs). Most of the
newly-detected sources are YSOs with gas envelopes which, based on their
luminosities, must contain objects with stellar masses $M_*\gtrsim8$ M$_\odot$.
Their spatial distribution spread over a $\sim12\times3$ pc region demonstrates
that Sgr B2 is experiencing an extended star formation event, not just an
isolated `starburst' within the protocluster regions. Using this new sample, we
examine star formation thresholds and surface density relations in Sgr B2.
While all of the YSOs reside in regions of high column density
($N(H_2)\gtrsim2\times10^{23}$ cm$^{-2}$), not all regions of high column
density contain YSOs. The observed column density threshold for star formation
is substantially higher than that in solar vicinity clouds, implying either
that high-mass star formation requires a higher column density or that any star
formation threshold in the CMZ must be higher than in nearby clouds. The
relation between the surface density of gas and stars is incompatible with
extrapolations from local clouds, and instead stellar densities in Sgr B2
follow a linear $\Sigma_*-\Sigma_{gas}$ relation, shallower than that observed
in local clouds. Together, these points suggest that a higher volume density
threshold is required to explain star formation in CMZ clouds.
