I'm not sure the Galaxy
class will be giving up its flagship status any time soon. Certainly there's no proof that the Sovereign
would be the inheritor.
Several sources erroneously claim that the NCC-1701-E would be the new Federation Flagship. However, none of the movies featuring that ship support such a claim.
For all we know, moving from the E-D to the E-E was a step down in Picard's career. Which would not be completely surprising, considering how the end of the E-D is somewhat ignominious, and how the first movie featuring the E-E indicated that Picard was in Starfleet disfavor and (along with his ship) all but banished...