I'm an ex-google employee laid off as part of the 12000.
To answer your question, basically not at all. Half a year before the layoffs, they explicitly consolidated power towards your direct managers around the assignment of work and especially quarterly and yearly assessment.
Not just toward managers in general -- before that point there was a consolidation of power towards managers in general over the years, but luckily a group of manager's peers would balance out or question any extreme examples, which moderated a lot of what can sometimes go wrong.
But right before the layoffs the system was changed to have an explicit emphasis on your direct manager.