Do you see any SEO risk here?
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Hi, Iām seeking your opinion regarding the issue we are facing during rebranding
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Hi there.
My, this is a lot of text

Well, I'll answer the question you are asking at the top: no, there shouldn't be risk of having live subdomain. However, everything you are talking about always is expected with rebranding - loss of traffic, dowgrading in rankings etc. So, what I'd recommend is, yes, to have a page on old domain, informing that you moved to another domain. however, I'd do it on main index page, not on subdomain, since who knows if you can even rank for that subdomain.
hope this helps.
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Great, thanks for help