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We report on NICER observations of the Magnetar SGR~1935+2154, covering its 2020 burst storm and long-term persistent emission evolution up to $\sim90$ days post outburst. During the first 1120~seconds taken on April 28 00:40:58 UTC we detect over 217 bursts, corresponding to a burst rate of $>0.2$ bursts s$^{-1}$. Three hours later the rate is at 0.008 bursts s$^{-1}$, remaining at a comparatively low level thereafter. The $T_{90}$ burst duration distribution peaks at 840~ms; the distribution of waiting times to the next burst is fit with a log-normal with an average of 2.1 s. The 1-10 keV burst spectra are well fit by a blackbody, with an average temperature and area of $kT=1.7$ keV and $R^2=53$ km$^2$. The differential burst fluence distribution over $\sim3$ orders of magnitude is well modeled with a power-law form $dN/dF\propto F^{-1.5\pm0.1}$. The source persistent emission pulse profile is double-peaked hours after the burst storm. We find that the bursts peak arrival times follow a uniform distribution in pulse phase, though the fast radio burst associated with the source aligns in phase with the brighter peak. We measure the source spin-down from heavy-cadence observations covering days 21 to 39 post-outburst, $\dotν=-3.72(3)\times10^{-12}$ Hz s$^{-1}$; a factor 2.7 larger than the value measured after the 2014 outburst. Finally, the persistent emission flux and blackbody temperature decrease rapidly in the early stages of the outburst, reaching quiescence 40 days later, while the size of the emitting area remains unchanged.