What is the typical sink rate during a well-executed carrier landing at the moment the main wheels touch the deck?
A lot. About 3-4 m/s (600-800 fpm). This is the speed at which 'normal' landing gear begin to break.

For carrier landings, there is no flare, so the touchdown speed equals to the sink rate on the final approach. The procedure in the linked question mentions 700 fpm.

We can arrive at a similar figure if we consider the standard carrier glideslope 3.5° (pdf) and the typical approach airspeed of ~120-130 kn. If we allow 20-30 kn for carrier speed and headwind, then for 100 kn (51.4 m/s) closing speed we get 51.4 m/s * sin 3.5° = 3.14 m/s ≈ 620 fpm.