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Unless there's actually a way to achieve FTL travel (I highly doubt it), you couldn't have interstellar empires. This video recognizes that it's difficult, when in reality it's probably impossible.
Generation (or sci-fi suspended animation, if possible) ships are the only way a species can move to another star system, but they won't have meaningful contact with their home world. They might be able to send messages back and forth that take decades to reach their destination, but that's about it and not very useful. At best they could share scientific advancements. The colony makes some breakthrough discovery and transmits it to the home world who can then apply it there and vice versa.