Hi, @Anthony Turner
Since I focus on Exchange Online, I know very little about AAD, as far as I know, Azure AD Connect typically requires that the local domain be validated in Azure AD. Since you mentioned that your local domain is not owned by you and cannot be used as a verified domain in a 365 tenant, it may not be straightforward to use AAD Connect in traditional hybrid mode with two different domains.
Importing a PST file into Exchange Online should not present any significant issues. For more information on how to import a pst file check out. Learn about importing organization PST files | Microsoft Learn
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