The Upside Down appears to be leaking from the gate Vecna created, however, and based on what the Upside Down is doing to the plant life in the finale, the Upside Down will likely be overtaking Hawkins and the rest of the world at a gradual pace. The flowers and other plant life of Hawkins is turning grey at the end of Stranger Things season 4 because the air in the Upside Down appears to drain the life out of everything they touch.
With Vecna being revealed as the mastermind behind everything that's happened in the show, his defeat would put an end to the threat of the Upside Down once and for all. Complicating this would be how, according to Will, Vecna didn't die, so he's bound to come back at some point and try to open the gate and allow for the Upside Down to destroy the world. The combined efforts of everyone were enough to defeat Vecna and stop him from making the Upside Down destroy the world, but a massive gate was still able to form in Hawkins that the Upside Down appears to be leaking out of.
Vecna wants to create enough gates to the Upside Down to allow her to enter Earth and destroy it. At the end of it all, Vecna is defeated, but they weren't able to stop his plans, and Hawkins is caught in the crossfire. The plant life of Hawkins turning grey appears to be an extension of this, and the larger-scale effects of it all are likely to be expanded on season 5. The end of the second volume of the show seems to promise the biggest shakeups to the show's status quo. There is very little information about season 5 at the moment, so everything about the finale will be speculative.
In addition to what it means for season 5, this is an explanation of everything that happened to Hawkins in the finale. There should be merit in discussing the ending of the show to build a hypothesis about what will happen in season 5. It would be appropriate for the show to end with a conclusion like that.
A field of flowers turning gray as an ash-like substance rains down from above is one of the last shots of season 4. The spores of the Upside Down will slowly kill everyone and everything they touch, with their radius of effect slowly increasing over time. All of the main characters end up learning about this even though they are scattered across the world.
It would be easy to conclude that Vecna won, but that is not the case.
There is an explanation of what happened to Hawkins at the end of the show. Max only temporarily died, so he wasn't able to bring the Upside Down to Earth. Everyone needs to figure out how to close the gate while dealing with the illnesses brought about by the spores. The environment of Upside Down is toxic to anyone other than native inhabitants. This is a breakdown of everything that happened in the finale of the show.
This makes for a clear setup for the fifth season of the show. Vecna wanted the Upside Down to come to Hawkins and overtake it. They come up with their own plans for saving the world.