I always assumed they were different souls due to both having different guiding trees. Was it ever stated otherwise?
It's right there in the title: Yakuza
Reincarnation. Also, she is repeatedly called a
Samsara user. (Samsara == reincarnation.) And it's noted that Samsara users bring change by bringing memories of their past lives.
Also were shown that the core personalities of Ryumatsu and Princess Ryuu are very similar. And shown that their reactions to getting soaked by Nui to be identical. (Back in the end of the circus arc, when Nui wakes up.)
Hint?: In chapter 3, we're told that Princess named the two pigbirds ("Usain" and "Bolt"). [But the official translation leaves that tidbit out.] In chapter 38, Coen is musing about the naming of the birds, but it's unclear from the scene who (princess, Coen, someone else?) named the birds. My best guess is that it
was Princess who named the birds. If so, that's a pretty clear indicator that she's a reincarnation. [Edited this paragraph after some double checking.]
However, the original setup definitely makes it look like Ryumatsu is a separate soul who gets put into princess body when she's an adult. And we're never told explicitly that given the two possibilities (two separate souls vs one soul, two personas) which one is the case. So "two souls" is not totally ruled out.
Two separate guiding trees can be explained by both theories.