We investigate the connection between X-ray and radio-loud AGNs and the physical properties of their evolved and massive host galaxies, focussing on the mass-related quenching channel followed by $mathcal{M}^star (simeq 10^{10.6} M_odot)$ galaxies in the rest-frame NUVrK colour diagram at $0.2 < z < 0.5$. While our results confirm that (1) radio-loud AGNs are predominantly hosted by already-quenched and very massive ($M_*>10^{11}M_odot$) galaxies, ruling out their feedback as a primary driver of $mathcal{M}^star$ galaxy quenching, we found that (2) X-ray AGNs affected by heavy obscuration of their soft X-ray emission are mostly hosted by $mathcal{M}^star$ galaxies that are in the process of quenching. This is consistent with a quenching scenario that involves mergers of (gas-poor) $mathcal{M}^star$ galaxies $after$ the onset of the quenching process, i.e., a scenario where $mathcal{M}^star$ galaxy mergers are not the cause but rather an aftermath of the quenching mechanism(s). In that respect, we discuss how our results may support a picture where the slow quenching of $mathcal{M}^star$ galaxies happens due to halo-halo mergers along cosmic filaments.
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