The distinction between different types of legitimacy such as input, output and throughput or process legitimacy is quite common in political science. Both input and output legitimacy refer to the substantial dimension of policy-making.
These frameworks have been influenced by Fritz W. Scharpf - see, e.g., the following working paper: https://www.mpi-fg-koeln.mpg.de/pu/workpap/wp98-2/wp98-2.html
You might also want to check the edited volume by J. Keulartz and G. Leistra on Legitimacy in European Nature Conservation Policy, to which I contributed a country study on Germany: https://www.springer.com/de/book/9781402065095
Concerning recent discussions on legitimcy issues in Scandinavia, the following paper could be interesting: Article Legitimacy and Efficiency in Planning Processes—(How) Does W...
yes, I am familiar with the pol sci discussion. Vivienne Schmidt has also written about this re. European integration from a more constructivist institutional perspective than Scharpf.
Some of the chapters in the Keulartz /Leistra book look very interesting.