Identification strategy for measuring impact of employee turnover on project quality
This looks challenging, and the following would only work in circumstances where:


Reliable estimates can be made of how long each completed project should have taken to complete.
Good records are maintained of the progress of individual projects, enabling assessments to be made of the form "Project A was X% complete after n years".


Suppose two projects that were estimated to require 3 years were actually completed in 5 years, and in both cases a project manager had moved on after 2 years.  One might then focus on how complete each project was at the time when the project manager left.  If one project was 70% complete at that time, and so took a further 3 years on the last 30%, that suggests Scenario 1.  If the other project was only 40% complete after 2 years, and subsequently progressed at the same speed taking a further 3 years on the remaining 60%, that suggests Scenario 3.