Plain text only is useful for me. But if different behaviour is useful for some of us, there are 2 solutions :
the user should choose the behaviour in the settings : by default the behaviour is the same than before : plain text only, but in options you can modify this behaviour : copy with formating, copy with url links ,....
Create different shortcuts for each action : ctrl + shift +v = plain text only , ctrl + alt + v = plain text with url , etc.... and make these shortcuts in the "edit" top menu.
In office excel there are already many copy/paste options it could be a source of inspiration
https://support.microsoft.com/en-us/help/291358/how-to-use-the-paste-options-button-in-excel