Powerful radio galaxies show evidence of ongoing active galactic nuclei (AGN) feedback, mainly in the form of fast, massive outflows. Yet, it is not clear how these outflows affect the star formation of their hosts. We investigated the different manifestations of AGN feedback in the evolved 3C 293 radio source, and in the young, reactivated 3C 236. Both sources harbor young star-forming regions and fast outflows of \hi and ionized gas. Due to the different evolution stages of these sources, they are expected to be at different phases of the AGNISM interaction process. Using high spatial resolution observations of CO lines taken with the IRAM Plateau de Bure interferometer, we studied the distribution and kinematics of the molecular gas in these sources, and compared the results with the dust and star-formation images of the host. We searched for signatures of outflow motions in the CO kinematics, and derived the star formation rate (SFR) and star formation efficiency (SFE) of the host with all available SFR tracers. Based on the gas mass derived from our observations and on the SFR estimates, we compared the star-formation efficiency of 3C 236 and 3C 293 against a sample of powerful radio galaxies. Our results suggest that the apparently low SFE of evolved radio galaxies is not necessarily due to AGN feedback, but may be caused by an underestimation of the SFR and/or an overestimation of the molecular gas densities in radio galaxies. Based on observations carried out with the IRAM Plateau de Bure Interferometer. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).