I bet the pollinators really appreciate all those little grooves while getting a drink!
Personally, I think this presents a great opportunity to practice some kintsugi in addition to the rock carving. Beeswax may stop the leak for a while but it will break down over time in addition to having a different expansion rate than the rock. There might be a mortar or concrete blend that would work as well, but you'd be best served calling your local hardscape suppliers to ask around about it. Off the shelf stuff might expand too much while curing, causing more damage.