Explaining orbital mechanics is hard because people aren't used to it, but I'll try. I'd recommend playing Kerbal Space Program if you really want to understand it though.

Orbiting is just moving horizontally as fast as gravity pulls you down, so you never fall down. If you speed the horizontal part up, you'll move further away on the opposite side of your orbit because you were moving sideways faster than you were falling down. To stay at that altitude you need to be moving faster though, so you'll fall back in if you don't accelerate here again. You don't just keep going further away, because higher orbits require faster and faster speeds.

Let me know if that helps, but this probably can't be understood by text very easily. You probably at least need pictures, if not video, but actually interacting with it is the best way. Kerbal Space Program is famous for helping people wrap their mind around orbital mechanics.

186 miles further from Earth, but at the end of its life in 2022 had moved it only 76 miles after it lost fuel.

My emphasis.
The satellite is orbiting Earth and to move further away from something you're orbiting, you need to raise your orbit. This basically means you need to go faster in the direction of orbit in order to move further from what you're orbiting.