It's important to remember the context of Discovery Season 3
Starfleet is to the Federation as the military is to whatever country launched them. That sponsoring country provides personnel, supplies, ships, shipyards, etc. So the United States military is funded by the United States. It's not a separate entity.
The we have The Federation. It's not states, but worlds, and these worlds are separated by vast differences. As Burnham notes, it's about "their shared vision". The Federation supported Starfleet, turning it into the entity we've seen in the 23rd and 24th centuries.
The problem Starfleet has is "The Burn", which destroyed virtually all the the ships of Starfleet and made dilithium exceptionally rare. As such, Starfleet is now cut off from most of the worlds that comprise the Federation without any apparent way to build ships or replenish dilithium. In fact, we see that they can't even keep their subspace relays operational. Starfleet is simply struggling to survive as an entity itself. This fits with what we're told by Book in S3E1, that the Federation just basically fell apart without starships in general to keep it together. We saw that again in S3E4, where Earth is now an autonomous (and somewhat xenophobic) government.
As such, without support from The Federation in any meaningful way, Starfleet became its own entity: a quasi-military entity without a mission beyond survival. What Saru means at the end is that Starfleet is now going to have to accept the ideals of The Federation again if it hopes to survive.