Satellites don’t have or need engines to keep them in orbit. Once launched at their elevation and velocity, there’s very little atmosphere to slow them down. They just go.
Imagine firing a bullet parallel to the ground. After the initial launch of the bullet from the explosion in the gun barrel, the bullet needs no engine to keep it going. It will slow down due to air resistance and hit the ground a few hundred or thousand feet away.
Now imagine that there was no air on Earth, like on the moon. When you fire the bullet parallel to the ground there will be no air resistance to slow it down. Nonetheless, it will still fall to the ground because even as the bullet goes forward gravity pulls it down.
But the Earth is also round, not flat. So if your bullet went fast enough the Earth would curve down as the bullet moved forward and the bullet would never hit the ground. It would be in orbit.
Once launched at orbital speed in the near vacuum of space a satellite just keeps going and going. Never slowing down because there’s practically no air resistance up there. But there’s still gravity up there pulling it down.
You are correct that it needs to maintain its orbital velocity. But it does keep initial velocity because of lack of air resistance to slow it down. As gravity tugs it down the curvature of the Earth falls away and the satellite keeps going round and round, in orbit, without any engines.
Even way up there, however, it’s not a complete vacuum. There’s hardly any air. It’s a near vacuum. But over time because there is some air, albeit almost none, it does slow down. That’s why satellites occasionally fall and burn up on their way down.