I headcanonon the Barsen'thor's Holocron is the same one in Mysteries of the Sith.

During the Shadow of Revan storyline on Rishi, each class story character gets their own personal mission. For the Barsen'thor, it's the chance to create their own Holocron with help from the Bothan Jedi Master Kutri O'a.

While building the Holocron, Master O'a presented you with several possible futures of those who would use your Holocron. One of those possibilities had the Barsen'thor's apprentice bury the Holocron in the forests of Sarkhai. Centuries later, a young girl who is a half-trained Jedi is angry the Republic has fallen and is driven by vengeance. She finds the Holocron on Sarkhai and demands the weapons she needs to fulfil her revenge.

In Star Wars: Mysteries of the Sith (MOTS), the New Republic is protecting a Jedi Holocron. The game doesn't explain where they got it from, but my theory is this is the Barsen'thor's Holocron. I theorize Kyle Katarn found it on Sarkhai during the Dark Empire saga and was angry the Republic had fallen, perhaps feeling frustrated since, from his perspective, everything he had fought for was for nothing since Palpatine's return erased years of progress in an instant. Combined with Kyle's Jedi training being incomplete, and he fits the description of the angry, half-trained Jedi. The fact he's a man and not a woman is a negligible difference since Master Yoda himself said the future is always in motion.

Plus, Kyle played fast and loose with the dark side on his path to become a Jedi, and even used dark side techniques like the Spear of Midnight Black to kill his enemies. As such, I could see him demanding the Holocron to give him the power he needed to topple the Dark Empire, and a dark sided Barsen'thor informing him of the Sith temple on Dromund Kaas, which also explains how Kyle learned about the Sith ruins. Also, Kyle could have learned Force Destruction from the Holocron, since he used it against Mara on Dromund Kaas.

The Barsen'thor's Holocron in SWTOR looks blue and pristine while the Holocron in MOTS looks brown and ancient. Which makes sense because, if this is the Barsen'thor's Holocron, it would have been weathered and worn down over the centuries.

In short, I believe the Jedi Holocron in Mysteries of the Sith is the same one the Barsen'thor created.