In the relativistic inertial frame of the thrown baseball, it'll not be accelerating, at first. But it will be accelerating at 9.81m/s² (along with the Earth's surface, and hopefully you) after it lands and is just sitting there. The inertial frame will have continued along its original geodesic into the ground, though (or rather, the frame is only instantaneously defined at the moment of the release, but the ball would have followed that path). If you can convince the ball to continue to not-accelerate indefinitely, NASA or Vought International may have a job for you.

In the Newtonian inertial frame of the "stationary" Earth, it accelerates downwards at 9.81m/s² until it hits the floor and comes to a stop and is no longer accelerating ("gravity", which is a thing here, and the normal force now summing to zero).

This is fairly academic for sporting goods, as if working with these two frames results in substantially different outcomes for you or your ball, your day is probably going badly, or at least fairly energetically, and baseball isn't your priority right now.