We propose the use of gravitational waves as a direct probe to break the NS-BH degeneracy as central engine of core-collapse supernovae. This degeneracy may be resolved by GW-calorimetry, given the $\sim 160$Mpc horizon distance to emissions of gravitational energy, $E_{GW}$, of the order of few\% $M_\odot c^2$, within the LIGO bandwidth of $<1$KHz. Here, we report on a deep search for gravitational radiation from the nearby event SN 2023ixf at 6.85\,Mpc. A black hole central engine is expected to reveal itself by a long-duration gravitational-wave chirp powered by BH spin-down. By universality of black holes, this signal is well-defined by mass-scaling of GW170817B powered by the low-mass black hole produced in delayed gravitational collapse following GW170817. Given the proximity of SN 2023ixf, a long-duration GW spin-down signal comparable to that inferred in GW170817B would have been detectable in the available data. The lack of detection of such signal disfavors central engines involving long-lived, rapidly rotating BHs and instead supports scenarios consistent with a NS remnant with the progenitor mass is likely below $\sim 20 M_\odot$.