As long it is orbiting the sun, i.e bound by the solar gravitational field then it is in the solar system?
Also depending how elliptical the orbit, is the perigee might be much closer than 700AU, while still being further than Pluto's orbit. For all we know 700 AU is the apogee and say the perigee is 70 AU (1.4x Pluto's apogee ).
The body must also be large enough to clear other bodies in the same orbit, except at the Trojan positions (L4 and L5), to be considered as a planet. Otherwise it would just be a Trans-Neptunian Object (TNO) or a Kuiper Belt Object (KBO) at these distances.
It obviously does in this case. But this pedantic detail is rather important. It was used to demote Pluto a few years back.
Does it? Would we actually know if there was another slightly more sparse belt at 700AU? If we can't track a large planet in that area, why would we be certain about the belt?
Alternatively, if it's an external object captured by the Sun, how would we even classify it as clearing or not if there's nothing to clear?
Well, apparently the object causes bunching of other bodies in the Kuiper belt. And it would have got enough time to complete a few orbits. I assume that at some point, the other objects on its orbit would have been thrown off course or consumed by the planet.
> how would we even classify it as clearing or not if there's nothing to clear?
I assume that it's based on mathematical modeling.