The rotation change is real.
However - from memory - the change is less than one second per century.
And who’s to say the weather gets colder in the next couple of centuries, and the days get longer? Climate change is always temporary, until the next change.
Looks like I’ll need to adjust my Daytimer.
Yes the length of a day has increased by (IIRC) a couple of milliseconds. Certainly measureable, but nothing of any practical consequence. This is in addition to the increase in length of day that is caused by the moon’s tidal friction (also around the same magnitude).
The new effect is caused by an increase in the earth’s rotational inertia about its axis of rotation. Moving mass further from the axis of rotation increases rotational inertia. Without an increase in angular momentum the result is a slower rotational speed. Angular momentum is equal to rotational speed x rotational inertia (analogous to the formula mass x speed for linear momentum). Angular momentum is conserved and no other body is involved. Therefore increasing inertia decreases speed.
This is a bit different than the other effect slowing the earth’s rotation. The tidal friction of the moon actually does reduce the angular momentum of the earth. Since angular momentum is conserved there must be a corresponding increase in angular momentum. This comes from an increase in the moon’s orbital angular momentum - the moon is getting farther away from earth. Again it’s a measureable effect but too small to have any practical significance.