I'm not sure I see full independence this early, but I can definitely see Earth taking a more hands-off approach towards Mars from here on. It seems like the situation ended with a negotiated settlement with Mars clearly having the upper hand; looked like the workers' families were allowed to come at the end (I'm guessing Lee's wife was already smuggled out of North Korea and could join the rest on booking passage to Mars; I really wish they'd show us more about how she escaped). Earth probably had to negotiate in good faith to get access to the asteroid's spoils. I don't see any viable way to militarily force Mars to fall in line; that would require a significant buildup of space-based military capabilities, and any one country trying that would immediately see everyone else crying foul (especially after the events of Season 2). Nor do I think making them submit by slowing or stopping resupply flights is viable; most or all of the resupply ships are owned and operated by Helios, and Dev is now on Mars. If no one else Helios on its own can keep the transport link to Mars open. So I could see a general amnesty for Dev, Ed, and the asteroid heist crew being agreed to. And there's the fact that the US in particular is dealing with the political fallout of allowing torture there (I can see the parallels to Abu Ghraib in OTL 2003).This is presumably why Morozova is being given the old KGB once over. Korzhenko is going to be looking for any donkey to pin the tail on once the abuses at Happy Valley come out, and Morozova, is an easy person to pin it on, she ordered the interrogations, backed Margo's suggestions and ultimately lost Russia and Earth the asteroid riches.
But yes, presumably there was some sort of declaration off screen, a fully independent city state or a client state of a neutral country. I guess we will find out in 18 months.
What I do predict for season 4 is that the Soviet Union and North Korea will have withdrawn from the M7 Alliance. The Soviets will probably blame the US for the asteroid heist, for letting it happen under their noses, for Margo, etc. And with the hardliner coup, they were already having increasing trouble getting along before it. The Cold War will probably restart to some extent. North Korea meanwhile nearly got its section of the base invaded, and Lee and his wife have seemingly defected by the end. A very bad look for them, and they'll probably blame the other M7 members and Helios for it.