  Supermassive black holes (SMBHs) which reside at the centres of galaxies can
inject vast amounts of energy into the surrounding gas and are thought to be a
viable mechanism to quench star-formation in massive galaxies. Here we study
the $10^{9\textrm{--}12.5}\,\mathrm{M_\odot}$ stellar mass central galaxy
population of the IllustrisTNG simulation, specifically the TNG100 and TNG300
volumes at \zeq{0}, and show how the three components -- SMBH, galaxy, and
circumgalactic medium (CGM) -- are interconnected in their evolution. We find
that gas entropy is a sensitive diagnostic of feedback injection. In
particular, we demonstrate how the onset of the low-accretion BH feedback mode,
realised in the IllustrisTNG model as a kinetic, BH-driven wind, leads not only
to star-formation quenching at stellar masses
$\gtrsim10^{10.5}\mathrm{M_\odot}$ but also to a change in thermodynamic
properties of the (\emph{non}-star-forming) gas, both within the galaxy and
beyond. The IllustrisTNG kinetic feedback from SMBHs increases the average gas
entropy, within the galaxy and in the CGM, lengthening typical gas cooling
times from $10\textrm{--}100\,\mathrm{Myr}$ to $1\textrm{--}10\,\mathrm{Gyr}$,
effectively ceasing ongoing star-formation and inhibiting radiative cooling and
future gas accretion. In practice, the same AGN feedback channel is
simultaneously `ejective' and `preventative' and leaves an imprint on the
temperature, density, entropy, and cooling times also in the outer reaches of
the gas halo, up to distances of several hundred kiloparsecs. In the
IllustrisTNG model, a long-lasting quenching state can occur for a
heterogeneous CGM, whereby the hot and dilute CGM gas of quiescent galaxies
contains regions of low-entropy gas with short cooling times.
