IMO, "Starfleet" is Earth's organization and always has been,
The problem with this assertion is that the Starfleet seen in TOS, TNG, DSN, and VOY is explicitly established to be the
Federation Starfleet on multiple occasions:
DSN: Tribunal: "O'BRIEN: I've been in service to the Federation Starfleet all my life. No one has ever questioned my loyalty."
VOY, Dark Frontier: "BORG: A vessel has been detected. Unimatrix four two four grid one one six. Activate. Alter course to intercept. Vessel identified. Federation Starfleet,
Intrepid class, one hundred forty-three life-forms. Prepare for assimilation."
TNG, The Most Toys: "This is not a mannequin. This is Data. This is formerly Lieutenant Commander Data of the Federation Starfleet. The only sentient android in existence."
And then there are the numerous references to Starfleet ships as "Federation starships" rather than "Earth starships:"
VOY, Initiations: "This is Commander Chakotay of the Federation starship
Voyager. Why have you fired on me?"
VOY, Equinox: "This is Captain Ransom of the Federation starship
Equinox. We're under attack. We need assistance."
STVI: "Send to Klingon High Command. 'This is
Excelsior, a Federation starship. We have monitored a large explosion in your sector. Do you require assistance?'"
DSN, Emissary: "On Stardate 43997, Captain Jean-Luc Picard of the Federation starship
Enterprise was kidnapped for six days by an invading force known as the Borg."
TNG, The
Pegasus: " I am Captain Jean-Luc Picard of the Federation starship
Enterprise."
DSN, For the Uniform: "You should have thought about that before you attacked a Federation starship."
TNG, The Ensigns of Command: "I am Lieutenant Commander Data of the Federation starship
Enterprise."
STV: "He requests that you send a Federation starship to parlay for our release at once."
And more.
And that's to say nothing of the fact that we see the Federation President, not the United Earth President or P.M., issuing orders to Starfleet in
Star Trek VI; of the fact that the Federation President is referred to as Starfleet's commander-in-chief in DSN: "Paradise Lost;" of the fact that we see the Federation President presiding over a Starfleet court-martial in
Star Trek IV; of the fact that we see Starfleet taking orders from the Federation Council in TNG: "The Defector;" etc.
There is no evidence whatsoever that the Starfleet seen outside of ENT is an Earth organization. It is the Federation Starfleet, not the United Earth Starfleet.
The logical conclusion is that when the writers created Starfleet in TOS Season One, they retconned the prior mentions of the
Enterprise belonging to other organizations out of continuity. ENT's scenic artists may have revived UESPA for their 22nd Century United Earth Starfleet, but the Federation Starfleet is clearly a different thing.