Taps have corresponding drill bits for their size. You shouldn't need to caliper measure the drill bit provided you're using the correct bit for that tap.
https://drillsandcutters.com/metric-...d-drill-chart/
There are different types of taps for different holes. Since this will (I think) be a blind hole you want a bottom tap.
https://www.cnccookbook.com/differen...uide-choosing/
Drill a smaller hole about the diameter of the divot you punched, then go up to the bit size that corresponds to your tap. This will help keep your hole centered. It looks like the mount itself can be used as a jig provided it's clamped properly but you might want a bushing to ensure you're new thread is perfectly centered. In fabrication it's often better to just make the job easier than to use more skill.
Mark your drill bit at the correct depth, or use a stop if you're using a press.