This is NOT a first and this is TYPICAL behavior in cold weather, and more specifically, with a cold battery pack.
The car will go into intentional charge / discharge repeat.... cycles to warm the battery pack.
When the car is charging, the RPM's go up. When the car is discharging, the RPM's go down. My car does this for 4-5 minutes each cycle.
After the battery pack internal temperature gets over 50'F this behavior should stop.
The 2000 to 2800 swings can be explained by this.
The 4000 when accelerating ( assuming it is generally lower ) means you where accelerating with a cold battery, and there was reduced battery assist, and thus the engine needed to work harder.
Now... if it does this on a 75 degree day.... come back and we'll talk more!