Was also able to extrude the resulting face now for 1 mm with the "Shell" tool. Don't understand why "Extrude" did just nothing though (would perhaps be helpful to give some textual hints which expectations of a function are not fulfilled instead of doing nothing). But got this working for now :)
Ok.(..) Still have to sync my expectation better to the way how things work in MoI. A lot is possible - just often not as I would expect. :) But that's ok for somebody who is still scratching the surface when it comes to actual modelling in MoI. (Am using MoI almost daily - but only as a super fast STEP viewer)
A couple of things are - try to use 2D profile curves and cutting things using boolean operations rather than trying to patch in surfaces on a 3D wire scaffolding and it's more common to construct things directly in place instead of say starting with a box and mutating its points into some other shape.