  Cosmic rays (CRs) may drive outflows and alter the phase structure of the
circumgalactic medium, with potentially important implications on galaxy
formation. However, these effects ultimately depend on the dominant mode of
transport of CRs within and around galaxies, which remains highly uncertain. To
explore potential observable constraints on CR transport, we investigate a set
of cosmological FIRE-2 CR-MHD simulations of L$_{\ast}$ galaxies which evolve
CRs with transport models motivated by self-confinement (SC) and extrinsic
turbulence (ET) paradigms. To first order, the synchrotron properties diverge
between SC and ET models due to a CR physics driven hysteresis. SC models show
a higher tendency to undergo `ejective' feedback events due to a runaway
buildup of CR pressure in dense gas due to the behavior of SC transport
scalings at extremal CR energy densities. The corresponding CR wind-driven
hysteresis results in brighter, smoother, and more extended synchrotron
emission in SC runs relative to ET and constant diffusion runs. The differences
in synchrotron arise from different morphology, ISM gas and \textbf{B}
properties, potentially ruling out SC as the dominant mode of CR transport in
typical star-forming L$_{\ast}$ galaxies, and indicating the potential for
non-thermal radio continuum observations to constrain CR transport physics.
