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Buy a decent set of bits and work up to 1mm oversize. Buy a brush for removing debris (yes, these are a thing). There are a number of resins that you can use to bond the metal tube into the rock.
I did a similar thing but the post had a 10mm threaded rod in it. I also put an electrical back box grommet between the wall and the post. Not sure how easy that rock is to drill from a picture though.
What do we reckon my chances are of drilling these stones for these brackets? They're the capping stones for my garden wall which should be getting placed this weekend. Plan was to drill for the brackets once they're on and mount a small trellis/ fence on top of the wall but I may well have underestimated the task.