  We experimentally investigate and utilize electrothermal feedback in a
microwave nanobolometer based on a normal-metal
($\mbox{Au}_{x}\mbox{Pd}_{1-x}$) nanowire with proximity-induced
superconductivity. The feedback couples the temperature and the electrical
degrees of freedom in the nanowire, which both absorbs the incoming microwave
radiation, and transduces the temperature change into a radio-frequency
electrical signal. We tune the feedback in situ and access both positive and
negative feedback regimes with rich nonlinear dynamics. In particular, strong
positive feedback leads to the emergence of two metastable electron temperature
states in the millikelvin range. We use these states for efficient threshold
detection of coherent 8.4 GHz microwave pulses containing approximately 200
photons on average, corresponding to $1.1 \mbox{ zJ} \approx 7.0 \mbox{ meV}$
of energy.
