We present initial results from the Polarisation Sky Survey of the Universe's Magnetism (POSSUM), analyzing 22817 Faraday Rotation Measures (RMs) with median uncertainties of 1.2rad/m^2^ across 1520 square degrees to study magnetized gas associated with 55 nearby galaxy groups (z~0.025) with halo masses between 10^12.5^ and 10^14.0^M_{sun}_. We identify two distinct gas phases: the Intragroup Medium (IGrM) within 0-2 splashback radii and the Warm-Hot Intergalactic Medium (WHIM) extending from 2 to 7 splashback radii. These phases enhance the standard deviation of residual (i.e., Galactic foreground RM-subtracted) RMs by 6.9+/-1.8rad/m^2^ and 4.2+/-1.2rad/m^2^, respectively. Estimated magnetic field strengths are several uG within the IGrM and 0.1-1uG in the WHIM. Our findings indicate that 'missing baryons' in the WHIM likely extend beyond the gravitational radii of group-mass halos to Mpc scales, consistent with large-scale, outflow-driven 'magnetized bubbles' seen in cosmological simulations. We demonstrate that RM grids are an effective method for detecting magnetized thermal gas at galaxy group interfaces and within the cosmic web. This approach complements X-ray and Sunyaev-Zel'dovich effect methods, and when combined with Fast Radio Burst Dispersion Measures, data from the full POSSUM survey - comprising approximately a million RMs - will allow direct magnetic field measurements to further our understanding of baryon circulation in these environments and the magnetised universe.