The instruction on box of tea bags I bought recently said do not re boil water. A bit of googling suggests its to do with reduced oxygen in the water.
I’ve always been properly unconvinced by this argument. True, the hotter water is, the less soluble oxygen (and carbon dioxide, and other gasses) are in it.
But this is a fixed amount, if you’re bringing it to 100oC again, gasses aren’t less soluble the second time around.
Maybe if you have hard water, and you use water that’s been repeatedly boiled, you get concentrated minerals?
Similarly unconvinced by this, at least in an electric kettle with an auto-cut-off.
For the amount of water that’s lost as steam, I can’t imagine that there’d be any discernable increase in concentration.
I could possibly believe that if your kettle is dirty, then re-boiling, or leaving water to sit in it for a long time would affect the taste noticably.