Honestly? Darth Vader is the very last person I would expect Sheev to tell about Byss. Palpatine (for the most part rightfully) held himself to be a better plotter, better manipulator, and better force user than basically anyone else in the galaxy. Byss was not made for if he lived long enough to die of old age, he could have just squirreled away his cloning facilities somewhere in the Imperial Palace for that. Byss was hidden so well because it was a fallback plan in case he was assassinated, and imho Palpatine would only have one man in mind as to who would be the one to do it.
The moffs? He can literally read their minds, he's spent the last two decades playing with them like his toys. The Rebellion? A joke, to the point that he showed up at Endor primarily to gloat. A Jedi? Possible but unlikely. But Vader, on the other hand? A very real threat, provided he ever found something to light a fire under his semi-robotic ass.
