  We present the results of a time-dependent search for neutrino flares in data
collected by IceCube between May 2011 and 2021. This data set contains
cascade-like events originating from charged-current electron neutrino and tau
neutrino interactions and all-flavor neutral-current interactions. IceCube's
previous all-sky searches for neutrino flares used data sets consisting of
track-like events originating from charged-current muon neutrino interactions.
The cascade data sets are statistically independent of the track data sets and
provide a new opportunity to observe the transient all-sky landscape. This
search uses the spatial, temporal, and energy information of the cascade-like
events to conduct searches for the most statistically significant neutrino
flares in the northern and southern skies. No statistically significant
time-dependent neutrino emission was observed. For the most statistically
significant location in the northern sky, $p_\mathrm{global} =$ 0.71, and in
the southern sky, $p_\mathrm{global} =$ 0.51. These results are compatible with
the background hypothesis. Assuming an E$^{-2.53}$ spectrum from the diffuse
astrophysical neutrino flux as measured with cascades, these results are used
to calculate upper limits at the 90\% confidence level on neutrino flares of
varying duration and constrain the contribution of these flares to the diffuse
astrophysical neutrino flux. These constraints are independent of a specified
class of astrophysical objects and show that multiple unresolved transient
sources may contribute to the diffuse astrophysical neutrino flux.
