@adamfilip I can think of a few more things to ask about and one thing to try (FWIW).
Is the layer shift always happening in the same direction? (I am wondering if it is always associated with a particular stepper?).
2.) When I had this problem with my previous printer, the nozzle was getting hung up on a protruding piece of plastic ( Z hop would often help but wasn't a reliable solution for me). This would happen when either:
the layers would start to curl up which was due to insufficient cooling (which sometimes just meant that the layer time was so brief that the previous layer had not sufficiently cooled when the next layer was extruded on top of it
or plastic built up on the nozzle and at some point the glob would stick to the print ( less likely with PLA because any PLA building up on the nozzle should melt vs for example a PET-G which is more like a gel when extruded)
or I was using some PLA filament that wasn't well suited for 3d printers.
You didn't sat what brand filament you are using, but if you are in the US, try eSun PLA+. You will want to run it at a higher temperature. It is not very expensive and very consistent roll to roll. I have thrown away almost full rolls of some PLAs because I couldn't count on them to behave in a predictable fashion.
All of the other points that folks have brought up are also great ideas to chase down.
Good luck hunting down the problem!