Did Bu Yeon finally left her body?

More likely.

What we know:

1. The specialty of a Jin mage is sealing magic
2. As a priestess, her power also comes from the heavens and can control souls (which more likely allowed her to take in Nak Su's soul while her own soul is still inside = two souls in one body)
3. Two souls, one body.

Bu Yeon can only "wake up" or to put it another way, relax in her sealing Nak Su's magic. Whenever Nak Su is sleeping, incapacitated, a soul ejector was activated, or they are within the lands of the Jin clan, those are the only times Bu Yeon manifests.

When Nak Su lost consciousness when Jin mama tried to kill her, Bu Yeon was able take control of her own body (she no longer have to keep Nak Su's powers sealed). The immense power of Bu Yeon came out in full force (her eyes showed a blue radiance again), called her mom, tears fell from eyes, and activated the ice stone afterwards.

It was not only because she missed her mother, more likely, it was also because it will be the last time they will ever meet each other. It was like Bu Yeon's final goodbye. It was Bu Yeon's "mom, thank you for everything, it is time for me to go, please take care of Mu Deok, I chose/changed her for you".

Why? Bu Yeon's main objective is the ice stone. She failed in her mission years ago when she was pushed to the Lake. Now, it is time to complete her objective (whatever it is -- maybe to return the ice stone to the heavens; or find someone worthy of controlling it, like Nak Su). Bu Yeon's first words were, "We did not lose it this time."

Now that the ice stone is in her reach, she finally activated it. Once activated, she left her own body and was finally able to talk to Nak Su face-to-face.

While talking, Nak Su asked if Bu Yeon is a Jin relic, to which Bu Yeon reacted with complete authority, "How dare a soul living off my body call me a relic?" If Bu Yeon was still sharing her body with Nak Su, it would have been, "How dare a soul sharing my body call me a relic?"

It is more likely then than Bu Yeon finally left her own body and left it to Nak Su's care:

1. She called her mom for one last time as her final goodbye
2. Her affinity with the ice stone (thanks to Jang Kang calling her soul back through the ice stone) allowed her to use the power of the ice stone and leave her own body -- and let Nak Su have full "ownership" instead of being a soul shifter == meaning, Bu Yeon's power is not just from the heavens--being a priestess--but also from the ice stone
3. Nak Su regaining her powers meant Bu Yeon is no longer in their body to seal her powers

At this point, Bu Yeon seems to trust Nak Su enough that she will make the right decisions and will not use the power of the ice stone like how "Nak Su the Assassin" would have had. She is no longer "Nak Su the Assassin", she is "Mu Deok". (And since her body is a Jin, she also becomes the heir, and can open the Jin vault. It wouldn't be surprising if she can also seal magic, a Jin clan specialty.)

I think the soul shifters can use their powers all because they are inside the ice stone's barrier, in return all the mages cannot use their magical abilities. Just like the Master Kang Soul Shifter who attacked them, soul shifters can freely use magic.

It is not because Buyeon left her body but because she cannot use her power to seal Naksu's power or perhaps she allowed it, as she said before ending her conversation with Naksu : "try it? try to endure it." referring to the burden the ice stone brings to it's owner.

For me, it is unfair and sad for Buyeon to end up leaving like in your theory. To just be left in the shadows, after all she is also a victim. Her power is used by Jin Mu to retrieve the ice stone, she lost her family,  she lost her way home and then soon lost her physical body too.