A new projpred paper by Yann McLatchie, Sölvi Rögnvaldsson, me, and @avehtari has been published on arXiv: [2306.15581] Robust and efficient projection predictive inference.
The main purpose of it is to present a workflow for projpred so that users may obtain reliable results in the least time-consuming way. But it also discusses the use of the projected posterior in causal settings and gives some more background in general.
Happy to receive feedback on it!