I would assume if I looked in the manual it would say to keep all 4 tires at the same tire pressure. I think shaving the tire would probably be the safest thing to do to get them an even tread depth, rather than running tires with different PSI.
Right now the left side tires on ours are 36psi cold and the right side are 35psi cold. It is difficult to have all 4 tires at the same pressure. I’m also assuming that the TPMS will consider a tire that is actually 35.6psi but shows as 36psi since it can be rounded up. With that in mind, I imagine the small differences in tread depth and tread pattern aren’t that big of a deal.
I am particular about my tires and tire pressure and constantly check/adjust them on all our vehicles. Although I suppose most people don’t check their tire pressure that often and run with under or possibly over inflated and under inflated tire pressures. I also assume car manufacturers understand this and allow their safety margins to include some variation in tire pressure (and tread depth/wear patterns as a result).
