One of the idea with “has the space around it cleared” is that the body has the right size and gravitational pull. The theoretical object in the Oort Cloud would relative fast clear the space around himself if it had the size to have a stable and long living internal heat source (that would either need lots of decaying nuclear material or would need to be at least about earth size to have enough stored energy to have a molten core).
So if you put earth into the Oort Cloud it would still be a planet, because we know that earth has the potential to clean it’s neighborhood. Not that our definition would be relevant, because Earth in the Oort Cloud would be a lifeless rock very fast, with nobody left to care about definitions.
Many million years is nothing in geological or astronomical timescales. Any (small) body with a heat source that short is dead cold by know. The solar system is 4.6 billion years old and the formation of planets or larger bodys has ended about 4 billion years ago.
And tidal forces mean that a way larger body is close by, like a gas giant, as far as I remember are all known body’s with tidal heating moons not planets.