How long is a earth day to the exact second?
The motion of Earth is very complicate and astronomers knows well.
If your question is how long does it takes the Earth to revolve on itself, this is 86400 in a remarkable stable way. The average error can be seen in this image from Wikipedia
So the Earth rotation is stable within few milliseconds. This is why, from time to time, we correct of one second a day, to compensate the accumulation of milliseconds in the years.
But if your request is "after how many seconds I will see the same stars in the same positions of yesterday?" the answer is the sidereal day, that is and that is
Why so different? While the Earth is rotating on itself, it is also rotating around the Sun, and the combination of the two motions is responsible of the time difference to see the same stars in the same positions.
So the answer depends on which day you want to consider.