I generally understood it as a lower FoS ( 1.5 v 3 ) means that there is more co fide ce in the accuracy of method.

Slopes are generally moment equilibrium so driving forced v resisting forces. You can calculate these forces and be reasonably confident (n geotech terms, which means they might be there they might now ). Also these methods have been well tested and proven to be satisfactory. Or there disadvantages have been established

FoS for bearing capacity failure probably could be lowered I would think but there may not be such a need for this when contact pressures and settlement generally govern.

I was looking at Google and there is a paper from Terzaghi titled "The actual factor of safety on foundations" in the UK's Institution of Structural Engineers, which I hope somebody may have a copy of it to share with us. Just looking at the title and considering that this paper is very old (30's), that paper may have some rationale about why a FOS of 3 is used in foundations.

Higher FOS means less movement - a batter slope may move a few hundreds mm horizontally while still has a FOS of 1.2-1.5. However if a footing supporting a building settles a few hundreds mm that could be a failure (10-20% of footing width)

Think about SF tower settlement - my take is it's a punching failure! Piles are not holding up the high rise.

Not sure if you can relate FOS with movement or settlements. As was pointed out above, FOS is just the relation between resistant forces to the acting forces. I guess that the FOS of 3 and 1.5 were picked based on actual observations of soil failures while keeping the design economically reasonable.