As a developer I feel my career advancement stagnating in its current trajectory.

This feels silly to ask, but is there merit to obtaining a masters degree as a software/design engineer to get to staff level one day?

My gut says experience and street cred matter way more but I'm curious what others think of the ROI.

father, husband, css golfer, ux engineer, silently defining variables as /sdv sdv.wtf

Would advise against getting a degree and instead seeking out a staff dev in the role you envision for yourself and who is willing to mentor you. You also need to be at a company with staff level project opportunities, which not all have.