Hello,
as my predecessors have already written, I would NEVER want to determine the residual moisture myself, as a mistake here can lead to considerable consequential costs.
The steps you listed are potentially critical for you, because the contractor is off the hook if the screed settles, continues to crack, the floor becomes uneven, or if it is just moist enough for the floor coverings to wave or detach.
Whether a screed has many or few (preferably none) cracks depends less on whether it is a new or old house, but rather on whether the work was done carefully and with good materials.
May I be curious and ask which company you are building with?
Regards,
Dirk