The narrow-line Seyfert 1 (NLSy1) galaxy, IRAS 17020+4544, is one of the few known sources exhibiting a multi-phase outflow in the highly ionized and molecular phases consistent with AGN feedback operating in the "energy-conserving" regime. We aim to characterize the properties of the ionized warm ionized gas in IRAS 17020+4544 using new optical integral-field spectroscopic (IFS) data, and to assess the presence of outflowing ionized gas and its connection with the other gas phases and its role in the AGN feedback. We analyze new optical seeing-limited IFS observations obtained with MEGARA at the Gran Telescopio Canarias (GTC) in both low- (R~6000; LR) and medium-resolution (R~12000; MR) modes. We model the H{alpha} and [OIII]{lambda}5007 emission lines using multi-Gaussian fitting to characterize in detail the ionized gas kinematics, particularly that of the ionized outflow, to derive its energetics and compare it with those of the X-ray and molecular phases. Diagnostic diagrams (WHAN, WHaD, and BPT) are used to investigate the dominant ionization mechanism. We identify a fast ionized outflow traced by both H{alpha} and [OIII] emission lines, with similar extensions (Rout~1kpc and ~0.5kpc, respectively) and velocities (vout~1460 and 1240km/s, respectively). A slower ionized outflow (vout~450km/s) is also detected in the secondary component of the [OIII] line. The fast outflow follows an "energy-conserving" regime in both H{alpha} and the [OIII] lines (from the LR setup), while the slower outflow follows a "momentum-driven" regime. The ionized outflows are enclosed within the molecular outflow detected with NOEMA (R_CO_=2.8+/-0.3kpc), and the large momentum boosts derived in both phases suggest efficient AGN feedback, likely dominated by radiatively driven winds (quasar-mode) rather than kinetic (jet-driven) processes. Ionization diagnostics indicate that the outflow is primarily AGN-driven, although a contribution from star formation- driven excitation cannot be ruled out, and some contribution from shocks cannot be excluded on smaller scales. Our results support a scenario where the multi-phase outflow in IRAS17020+4544 is AGN-driven and "energy-conserving" in the different (i.e., highly ionized, warm ionized and molecular) phases, efficiently coupling the AGN energy to the host galaxy's interstellar medium. The molecular outflow appears to be the dominant phase, while the ionized phase contributes less to the mass budget and feedback efficiency.