Supermassive black holes (SMBHs) are often treated as self-regulating enginesthat couple accretion inflow to feedback outflow and help stabilise their hostgalaxies. In the Milky Way, Sgr~A* is currently underluminous compared toclassical active nuclei, raising the question of whether it is a pathologicaloutlier or a typical, slowly flickering regulator. This work tests this ideain a falsification-first way, using Milky Way analogues and Sgr~A*--mass blackholes in the TNG300-1 cosmological simulation together with Milky Way--massgalaxies from SDSS, GAMA and MaNGA. At $z\simeq 0$ a dimensionless \emph{static homeostasis} proxy is defined as$\Lambda_0 \equiv g_{\rm BH}/g_\star$, the ratio of black-hole specific growthrate to stellar specific growth rate. A \emph{homeostatic band}$-5 \le \lambda_0 \le 3$ in $\lambda_0=\log_{10}\Lambda_0$ is identified forMilky Way--mass hosts in TNG300, containing $4960$ Milky Way analogues and$115$ Sgr~A* analogues. Within this band the medians are$\tilde{\lambda}_{0,{\rm MW}}=-1.28$ and$\tilde{\lambda}_{0,{\rm SAG}}=-0.96$, a factor $\simeq 2$ difference in$\Lambda_0$. Kolmogorov--Smirnov and permutation tests reject the nullhypothesis that the two subsets are drawn from the same $\lambda_0$distribution. The offset is larger and more significant in the star-formingsubsample and does not vanish when hosts are split by specific star-formationrate. Time-domain homeostasis is probed using black-hole growth tracks$\Lambda_{\rm BH}(t)=\dot{M}_{\rm BH}(t)/M_{\rm BH}(t)$ from the TNGblack-hole details catalogue. Sgr~A*--mass and slightly more massive controlblack holes follow a common evolutionary sequence that drifts from burstyearly growth towards more negative, regulated values at late times, withoverlapping percentile bands. Typical time-domain homeostasis does not dependstrongly on the presence or absence of major mergers within currentstatistics. The central result concerns the \emph{variance} of $\lambda_0$ as a functionof black-hole mass. For TNG Milky Way analogues, the variance of$\lambda_0$ over the mass interval$5 \le \log_{10}(M_{\rm BH}/M_\odot) \le 9$ follows${\rm Var}(\lambda_0) \simeq a + b \log_{10}(M_{\rm BH}/M_\odot)$ with$b \simeq -0.27$. More massive black holes therefore sit in a regime ofsmaller homeostatic variance: the central engine acts as a \emph{stifferthermostat}. High-fidelity observational Milky Way--mass samples from GAMA andMaNGA show variance slopes that are negative but shallow, consistent in signwith the TNG prediction within uncertainties, while SDSS DR8 shows a weakpositive slope $\simeq +0.10$ that is plausibly dominated by proxy noise inblack-hole mass and accretion at the high-mass end. A simple summary tableshows that TNG and GAMA agree that variance declines with $M_{\rm BH}$, SDSSdoes not, and MaNGA is consistent but limited by small $N$. In this picture Sgr~A*, with $M_{\rm BH}\simeq 4\times10^6\,M_\odot$,occupies the high-variance, ``loose thermostat'' regime: the Milky Way isexpected to wander further from its median homeostatic state than galaxieswith $10^8\,M_\odot$ black holes. This reconciles its current quiescence withevidence for recent energetic activity without treating Sgr~A* as broken. Atthe same time, the absolute normalisation of $\Lambda_0$ reveals a tension:Milky Way analogues in TNG sit at much lower $\Lambda_0$ than those in SDSSand GAMA, indicating that the simulation underpredicts specific black-holegrowth at fixed stellar growth. The main conclusion is that the \emph{trend}of decreasing variance with $M_{\rm BH}$ is likely real and is now detected,but the absolute level of accretion in Milky Way--mass galaxies remains a keydifference between current simulations and data.