  Bose mixture quantum droplets display a fascinating stability that relies on
quantum fluctuations to prevent collapse driven by mean-field effects. Most
droplet research focuses on untrapped or weakly trapped scenarios, where the
droplets exhibit a liquid-like flat density profile. When weakly trapped
droplets rotate, they usually respond through center-of-mass motion or
splitting instability. Here, we study rapidly rotating droplets in the strong
external confinement limit where the external potential prevents splitting and
the center-of-mass excitation. We find that quantum droplets form a triangular
vortex lattice as in single-component repulsive Bose-Einstein condensates
(BEC), but the overall density follows the analytical Thomas-Fermi profile
obtained from a cubic equation. We observe three significant differences
between rapidly rotating droplets and repulsive BECs. First, the vortex core
size changes markedly at finite density, visible in numerically obtained
density profiles. We analytically estimate the vortex core sizes from the
droplets' coherence length and find good agreement with the numerical results.
Second, the change in the density profile gives a slight but observable
distortion to the lattice, which agrees with the distortion expected due to
nonuniform superfluid density. Lastly, unlike a repulsive BEC, which expands
substantially as the rotation frequency approaches the trapping frequency,
rapidly rotating droplets show only a fractional change in their size. We argue
that this last point can be used to create clouds with lower filling factors,
which may facilitate reaching the elusive strongly correlated regime.
