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Your request was specific to surface but I wasn't sure you if you meant the edge of a surface. There are a variety of methods to extrude a face to a distance or location. I have attached a video to show the Snap To functionality that allows a distance value to be infered after indicating a parallel plane. There is also the ability to Extend To which will find the intersection of the extend and an object or Extend All which will extend to any objects along the extrude path.
If you meant surface edge, for Fusion there is a difference between extrude and extend. Extend which exists in the Modify dropdown of the Patch workspace will support extending the edge Natural, Tangent or Perpendicular to the edge. It will take a value input like the Snap To but doesn't automate the trimming operation which may be what you are interested in?
Can you give a bit more detail on which you want to be able to do?
If you imagine extending the rectangular prism into a bowl so the prism has to extend through the body in order to contact all of a surface. For now, we've just been extruding then splitting or doing a boolean cut but that leaves us with extra steps and more junk to delete, and it seems like a common enough operation that it might be useful for lots of people (assuming I'm not missing something obvious)
Incidentally I couldn't help but notice the error message toward the end of that 🙂
This i think solves it. When you invoke the extrude command and change the Extents to To, you have to click on the arrow once and then the surface you want to extrude to.