It was pretty long-shot, true. Sorry that it doesn't work; I can't open it myself either anymore.
It really does seem like Godot doesn't have support for this kind of thing yet. Maybe add a feature request on the github page?
Potential solutions I could think of:
You could draw custom shapes in Godot, this page is your friend for that: https://docs.godotengine.org/en/3.2/tutorials/2d/custom_drawing_in_2d.html
It would be a lot of work, but you could do something like add a layer on top of your text and draw shapes that mimic underlined texts and strikethroughs. Not a great solution though, tbh.
A simpler solution might be to have three separate fonts: A normal one, one that is underlined and one that is strikethrough. And then you change the font whenever needed. BBCode does allow you to override the custom font in specific places, I guess that would be the most straightforward approach. You can find lots of tutorials online on making your own fonts, still not a great solution; but I guess an acceptable workaround.