Very good post. I did jump, and I found it fairly easy, because my basis in brand strategy lied broadly on reputation and promises/values, leaving the sheer “advertising” aside.
I don’t agree in marginalizing semiotics: I think it‘s still a core part of the user experience, because users need to understand and interact with an organized system (a sophisticated architecture, a step-by-step process, a chat-bot).
Also, branding, as you mentioned, provides identification, and identity is the other subject of the experience: not always a “company” anymore, but a system, a collective, a representative. They are all branded, their recognition/characters/values are part of the experience (design).
This is why I see branding and UX very close to each other, and sometimes I even kind of mistrust a UX who doesn’t know anything about branding.