Why we can accurately detect stars billions of light years away, but we can’t confirm if we have a 9th planet in our solar system?
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With respect to the one (and AFIK only) star we have seen billions of light years away, it is pure happenstance that the universe magnified its light such that we could detect it.
Secondly, we have disproved many proposed additional planets.
Finally, some notes on planet hunting. You can see a star because it is bright. Planets aren’t bright, so when you look at them (within our solar system) you only see them because they reflect light from the Sun. The further away the planet, the less sunlight reaches it to be reflected, and the dimmer the reflected light is when it reaches Earth. This makes direct observation of distant planets difficult to impossible. The planets beyond Neptune were initially detected because of the gravitational effect they have on planets we can see. However, like with light, the smaller and more distant the body is, the smaller its influence on other planets and therefore the harder it is to detect. So while it is easy to disprove the existence of a large planet close to Neptune, it is difficult to disprove a small planet which is much further out.
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