  The Heisenberg triangular lattice quantum spin liquid and the phase
transitions to nearby magnetic orders have received much theoretical attention,
but clear experimental manifestations of these states are rare. This work
investigates a new spin-half Yb$^{3+}$ delafossite material, KYbSe$_2$, whose
inelastic neutron scattering spectra reveal a diffuse continuum with a sharp
lower bound. Applying entanglement witnesses to the data reveals significant
multipartite entanglement spread between its neighbors, and analysis of its
magnetic exchange couplings shows close proximity to the triangular lattice
Heisenberg quantum spin liquid. Key features of the data are reproduced by
Schwinger-boson theory and tensor network calculations with a significant
second-neighbor coupling $J_2$. The strength of the dynamical structure factor
at the $K$ point shows a scaling collapse in $\hbar\omega/k_\mathrm{B}T$ down
to 0.3 K, indicating a second-order quantum phase transition. Comparing this to
previous theoretical work suggests that the proximate phase at larger $J_2$ is
a gapped $\mathbb{Z}_2$ spin liquid, resolving a long-debated issue. We thus
show that KYbSe$_2$ is close to a spin liquid phase, which in turn sheds light
on the theoretical phase diagram itself.
