  The nematic electronic state and its associated nematic critical fluctuations
have emerged as potential candidates for superconducting pairing in various
unconventional superconductors. However, in most materials their coexistence
with other magnetically-ordered phases poses significant challenges in
establishing their importance. Here, by combining chemical and hydrostatic
physical pressure in FeSe$_{0.89}$S$_{0.11}$, we provide a unique access to a
clean nematic quantum phase transition in the absence of a long-range magnetic
order. We find that in the proximity of the nematic phase transition, there is
an unusual non-Fermi liquid behavior in resistivity at high temperatures that
evolves into a Fermi liquid behaviour at the lowest temperatures. From quantum
oscillations in high magnetic fields, we trace the evolution of the Fermi
surface and electronic correlations as a function of applied pressure. We
detect experimentally a Lifshitz transition that separates two distinct
superconducting regions: one emerging from the nematic electronic phase with a
small Fermi surface and strong electronic correlations and the other one with a
large Fermi surface and weak correlations that promotes nesting and
stabilization of a magnetically-ordered phase at high pressures. The lack of
mass divergence suggests that the nematic critical fluctuations are quenched by
the strong coupling to the lattice. This establishes that superconductivity is
not enhanced at the nematic quantum phase transition in the absence of magnetic
order.
