I did some testing in the past few days: I've been reinstalling everything a few times and I tried to keep everything to a bare minimum (I did have the 'less real than realism' mod installed every time), but the problem did persist unfortunately . There was no way to select another configuration or click the '+' in the above screenshot which means that all engines were stuck in their base configuration and level. The screen did appear normal though.
I then started another install with realism overhaul and rp-1 via ckan (just following the install guide and not adding anything else) and this did result in a working upgrade screen where I could click configuration and tech levels. There were also tech nodes in the tech tree for the engine upgrades and I did not see those in my LRTR install, which makes me believe that it might be caused by wrong or missing tech registration in the LRTR tech tree.