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In the age of large-scale galaxy and lensing surveys, such as DESI, Euclid, Roman, and Rubin, we stand poised to usher in a transformative new phase of data-driven cosmology. To fully harness the capabilities of these surveys, it is critical to constrain the poorly understood influence of baryon feedback physics on the matter power spectrum. We investigate the use of a powerful and novel cosmological probe, fast radio bursts (FRBs), to capture baryonic effects on the matter power spectrum, leveraging simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (or CAMELS) project, including IllustrisTNG, SIMBA, and Astrid. We find that FRB statistics exhibit a strong correlation, independent of the subgrid model and cosmology, with quantities known to encapsulate baryonic impacts on the matter power spectrum, such as baryon spread and the halo baryon fraction. We propose an innovative method utilizing FRB observations to quantify the effects of feedback physics and enhance weak-lensing measurements of S8. We outline the necessary steps to prepare for the imminent detection of large FRB populations in the coming years, focusing on understanding the redshift evolution of FRB observables and mitigating the effects of cosmic variance.