The Embassy is a completely different holding and doesn't affect the starbase at all. If you look at the image below you'll see that the Embassy and Starbase each have their own tabs on the left side.
When you click on the Starbase tab you will see the same project list that we've seen the past few months (wow can't believe it has been a few months already). When you click on the Embassy tab you'll see a similar window except for the Embassy. If I recall correctly there are only 3 project slots. Two regular and one special. I could be mistaken since I'm not in the game right now to look at it, but I'm pretty sure that's how it is set up.
Each one works independently from the other, so working on the Embassy won't slow down progress on the starbase. What is also nice about this is that we will be working on more projects at the same time which means players will have more opportunities to earn fleet credits.
I didn't really check. I'm going to assume we'll have to reach certain tiers just to unlock those things. If they are even in the embassy. They do exist on New Romulus at the beam in point so it is very easy for players to just use those.
The one thing that I am happy about is in the embassy there is an actual office with two desks for James and I lol