That gear (a) steps and repeats all the construction geometry, not just the final tooth form, and (b) assembles all the teeth together as solid Boolean operations, instead of just piecing together curves. So with some small changes, the regeneration time and entity count can be greatly reduced, as attached.

Though hit testing could be improved too. You could accelerate the existing code with a bounding box test, or with an O(log n) data structure for the entities, but either of those would add complexity. The simplest option might be to let gl do the test with a selection buffer. That might even be a net reduction in lines of code, and might benefit naturally from any later work to speed up rendering.

gear_faster2 still steps and repeats the construction geometry; so you have one copy per tooth of all the circles and stuff, even though they're all exactly coincident. So regeneration is faster, but entity selection is still slow.

I was lazy and just retraced the tooth form in a second group, since you'd already sketched it in the first one. The cleanest way to draw the gear would be to put only the construction geometry in one group, put the tooth form in a second group, and then step and repeat the second group. That's fast, avoids duplication, and also makes the constraints easier to follow (since the tooth form can depend on the construction geometry but not vice versa).