Energetic feedback by Active Galactic Nuclei (AGNs) plays an important evolutionary role in the regulation of star formation (SF) on galactic scales. However, the effects of this feedback as a function of redshift and galaxy properties such as mass, environment and cold gas content remain poorly understood. The broad frequency coverage (1 to 116 GHz), high sensitivity (up to ten times higher than the Karl G. Jansky Very Large Array), and superb angular resolution (maximum baselines of at least a few hundred km) of the proposed next generation Very Large Array (ngVLA) are uniquely poised to revolutionize our understanding of AGNs and their role in galaxy evolution. Here, we provide an overview of the science related to AGN feedback that will be possible in the ngVLA era and present new continuum ngVLA imaging simulations of resolved radio jets spanning a wide range of intrinsic extents. We also consider key computational challenges and discuss exciting opportunities for multi-wavelength synergy with other next-generation instruments, such as the Square Kilometer Array and the James Webb Space Telescope. The unique combination of high-resolution, large collecting area, and wide frequency range will enable significant advancements in our understanding of the effects of jet-driven feedback on sub-galactic scales, particularly for sources with extents of a few pc to a few kpc such as young and/or lower-power radio AGNs, AGNs hosted by low-mass galaxies, radio jets that are interacting strongly with the interstellar medium of the host galaxy, and AGNs at high redshift.