How to identify the object with mass range of $(2.2-3)M_\odot$ in the merger of compact star systems

High-frequency gravitational-wave (GW) radiation has been detected by LIGO-Virgo-KAGRA in the merger of compact stars. However, two GW events, GW190814 and GW200210, the mass of one companion object falls into the mass region of $(2.2-3)\rm~M_\odot$, and how to identify such object (e.g., as a low-mass black hole (BH) or a massive neutron star (NS)) remains an open question. In this paper, we propose a method to identify the mystery compact object (MCO) with the mass region of $(2.2-3)\rm~M_\odot$ in a binary system via the possible electromagnetic (EM) radiations before and after the mergers. A multi-band EM emission can be produced with $L\propto(-t)^{7/4}$ (or $L\propto(-t)^{-5/4}$) during the inspiral phase due to the BH battery (or interaction magnetospheres) mechanism, and a bright (or dark) kilonova emission is powered by radioactive decay with ejecta mass ratio $q>1.7$ (or $q<1.7$) during the post-merge state when MCO is as a low-mass BH (or massive NS) to merger with NS. Moreover, by considering the merger system between MCO and a BH when MCO is a massive NS, we find that it requires the BH with high spin (e.g., $a\sim0.8-0.99$) to make sure the tidal disruption event (TDE) occurred, and a multi-band precursor emission and bright kilonova emission can also be produced during the inspiral phase and post-merge state, respectively. In any case, no matter which mechanism we adopt, such precursor emissions are too weak to be detected by most current telescopes unless the distance is close enough.