I think having them as 2 separate buttons may be a little unnecessary. Maybe having 1 link that comes to this page with a google form-type thing on the side for more private feedback messages? This really isn't a big deal, but I wanted to know if there was a benefit to having an email link be a separate button, other than maybe some file flexibility? I really don't know and would like to hear more about it!

edit: it'd probably actually make more sense as a 3rd tab at the top, rather than a floating sidebar lol