Do you re-heat the kettle between pours?

Short answer: No

By reheating your kettle between pours you introduce another variable which can mess with the consistency of your brew. The reason we measure everything when brewing coffee is to be able to isolate a single variable, adjust it, and determine its impact on the taste of the brew. Consistency is the most important thing here. Losing one or two degrees in your kettle while brewing shouldn't have much of an impact on the taste of your brew if it happens consistently. Also, the water drops in temperature significantly when it reaches the grounds, as explained in James's video you probably meant.

Both James Hoffmann and Matt Perger recommend using boiling water for brewing because seeing water bubble (and therefore knowing it's exactly 100°C) is more reliable than having a thermometer telling you the temperature. "25 degree water looks exactly the same as 85 degree water".

My recommendation is to let the water come to a boil and as soon as it starts boiling, start your brew and don't reheat it between pours. Even though the water might cool down a little, it will do so similarly from brew to brew. If you reheat your kettle between pours, you'll have to put in on the stove the exact same way each time, which is difficult (maybe not difficult but surely finicky) to achieve, especially if you have a pour-over to worry about.

Now, before anyone comments with "100°C is too hot, you'll burn the coffee":

Coffee is roasted at temperatures around and above 200°C, you're not burning anything.

"It will taste burnt and bitter because the bitter compounds will be extracted more easily."

In that case, over-extraction is your problem which can easily be solved by adjusting your grind size.