Can Sump pump basin depth cause damage
You done good.
It's doing its job and no risk of damage; sounds like you set it up perfect. The reason for more frequent kicks is for every increment you go deeper, you add that much more water spilling into the bucket but a sump float has a fixed height it kicks on. Your flow rate went up; the good news us you're draining more water from your basement than before which can add a nice bit of buffer relieving water further back from your sump pit than before.