I understand that you are asking about the differences between docking of metal complexes and docking of organic compounds.
Since metal complexes are different in many respects such as high-speed spin transitions, high electron density, etc., they usually do not give accurate results in force fields using classical mechanics. However, technology is advancing and many problems can be overcome through deep learning. It is possible to find papers on this subject in important places such as ACS. Nevertheless, the presence of metal atoms is an important factor affecting the accuracy of molecular docking. If the metal atoms are surrounded by ligand atoms in such a way that they do not have any connection with the protein surface, good and physically equivalent results can be obtained if the electronic configuration of the metal atom is "ignored". I do not think that molecular mechanics will give very accurate results if the metal atom is in contact with the protein. This is of course closely related to the force field used. OPLS4 force field can give successful results in metal interactions. OPLS5 is likely to get better results as it will contain quantum mechanical parameters.
In terms of software, if the software you use does not have the necessary metal atom parameters by default, the software will perform the calculation when you enter the parameters of this metal atom into the software. What is important here is that a partial charge assignment to the metal atom is also realised. If there are no partial charges on the metal atom, the software gives an error. Metal atoms in metalloproteins such as zinc usually come with default parameters since the interaction of organic compounds with these metal atoms in the protein structure will be evaluated, but it is common for many metals not to have parameters, especially in free software.