That history was not expanded on that much. Besides, Mando season 2 feels like they just met. Baylon is more familiar with Ahsoka, as he is with Anakin. Baylon did use his words to bring Ahsoka down a peg in their first fight.

The same can be said for Baylan and Ahsoka, their history isn't expanded either and they never met before the events of Ahsoka.

But he did strike her on an emotional level, something Morgan has NOT done.

Like, no he didn't. His apprentice had more history with Ahsoka than Baylan and did more to hurt Ahsoka emotionally than Baylan.

How exactly? Injuring Sabine doesn't count, as Ahsoka arrived in time to give Sabine the treatment she needed. Skoll accused Ahsoka of abaondoning Anakin, which brought back Ahsoka's memory of that vision on Lothal. She may have kept a pokerface, but it did effect her on the inside. She was able to recover after her lesson with Anakin on the WBW however. There might be more in the next season. Skoll is likely going to be more dangerous than Morgan too.

How is that enough to make him Ahsoka's archnemesis? And her being affected by Baylan's words isn't even explored enough to make him archnemesis worthy. In fact, Baylan knowing about Anakin being Darth Vader is a massive plot hole as Palpatine made sure no one knew his true identity. So him accusing Ahsoka of abandoning Anakin makes no sense.

Saying Palpatine made sure no one knew Vader's true identity is like saying Order 66 was foolproof. Besides, Thrawn and Tarkin knew.

Tarkin and Thrawn held so much significant power within The Empire that Palpatine deemed them trustworthy enough to know Vader's true identity and live. Tarkin fought alongside Anakin during the Clone Wars so he would have been able to recognize Anakin's fighting style and personality, which would help him deduce he is Darth Vader. And Thrawn is one of the most tactical geniuses in The Galaxy and exceptional in identifying patterns. This was a bad example to use.

I am also pretty sure a few Inquisitors knew, like the Grand one. Keeping someone's identity hidden is not always foolproof. Maybe we might learn that Skoll was at the Jedi Temple during the sacking and saw Anakin. Then he encountered him as Vader somewhere. Both encounters playing a role in his fall.

The Grand Inquisitor does not know Vader is Anakin. A select few people knew Vader was Anakin, most were considered outlaws to The Empire. Palpatine had eyes and ears everywhere within The Empire. Realistically, Baylan would have been assassinated or on the run before the events of Ahsoka and is only alive because Filoni and Disney Lucasfilms could not care less about lore consistency.