What is the typical sink rate during a well-executed carrier landing at the moment the main wheels touch the deck? And how has this changed over the decades?
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.
it’s dependent upon the aircraft in question and the approach speed that they need to use, but assuming a fighter aircraft like an F-18 with an approach speed somewhere in the neighborhood of 130 knots, a typical 3.5° glideslope to impact yields a descent rate on somewhere between 600-700fpm. The faster the ship is moving and the greater the surface winds it’s steaming into, the lower the vertical speed will be on glide path to touchdown.