It seems that currently, it’s not possible to customize the icon’s custom links because the hamburger menu decoration method doesn’t take into account the prefixValue constant (which contains the icon’s name) or something like that…
It also seems to me that hamburger-menu decorations with api.decorateWidget are going to be depreciated. See:
Also, the fact that external links don’t work anymore could come from this:
So that there should be some changes in core to make this available.
My knowledge of how Discourse works is almost non-existent so I could be very wrong.