The thermal Sunyaev-Zeldovich (SZ) effect and soft X-ray emission are routinely observed around massive galaxies and in galaxy groups and clusters. We study these observational diagnostics of galaxy haloes for a suite of cosmological `zoom-in simulations from the `Feedback In Realistic Environments project, which spans a large range in halo mass 10^10-10^13 Msun). We explore the effect of stellar feedback on the hot gas observables. The properties of our simulated groups, such as baryon fractions, SZ flux, and X-ray luminosities (L_X), are broadly consistent with existing observations, even though feedback from active galactic nuclei is not included. We make predictions for future observations of lower-mass objects for both SZ and diffuse X-ray measurements, finding that they are not just scaled-do