Amino-functionalized P(V) derivatives providing both N- and O-donor modes have attracted interest owing to their potential to form interesting coordination assemblies with applications such as biological drugs. Novel coordination modes of two- and four-dentate tris (pyridin-2-yl)phosphoric triamide OP[NH-$^2$Py]$_3$ as ([Co(II){[O][NH-$^2$Py]P(O)[Ph]}$_2$(DMF)$_2$], 1) and ([Cu(II)Cl{[NH-$^2$Py]$_2$P(O)[N-$^2$Py]}].DMF, 2) have been synthesized and structurally studied. The metal center environment is distorted octahedral for 1 and distorted square pyramidal for 2. The crystal structure of a new complex of Cu(II) with a Cu[N]$_4$[Cl]$_2$ environment ([Cu(II)Cl$_2$(Pyrazole)$_4$], 3) is also investigated. An evaluation of the inhibitory effect against the coronavirus (Main Protease [MPro] of SARS-CoV-2) was carried out by a molecular docking study and illustrates that these compounds have a good interaction tendency with CoV-2, where 1 has the best binding affinity with the biological target comparable with other SARS-CoV-2 drugs. Moreover, theoretical QTAIM and natural bond orbital (NBO) calculations are used to evaluate the metal-oxygen/-nitrogen bonds suggesting that they are mainly electrostatic in nature with a slight covalent contribution. A molecular packing analysis using Hirshfeld surface (HS) analysis shows that N—H … O (in 1 and 2) and N—H … Cl (in 3) hydrogen bonds are the dominant interactions that contribute to the crystal packing cohesion. The semi-empirical PIXEL method indicates that the electrostatic and repulsion energy components in the structures of 1 and 2 and the dispersion and electrostatic components in that of 3 are the major contributors to the total lattice energy