What are the precision characteristics of Google S2 for let’s say two indexed points which are within a radius of 5km? What kind of precision can I expect in mm for a query for these points?
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It depends on the S2 level on which you've indexed these points. Not all cells on a given level are the same size, but on average they'll all be close.
For example, a level 30 cell (smallest level) is on average 74 mm^2, so it's very precise.
You can see a reference here.