There are two main ways we detect exoplanets. The primary way that I believe accounts for the vast majority of planets we have detected is the transit method. Basically we watch the light from a star very closely and look for a dip in the amount of light coming from it as a planet transits in between us and the star. This of course depends on the planet to pass directly between us and the star, and that means that its ecliptic plane has to be directly edge on with us. The second method is that we are able to detect minor wobbles in a star that infers that there is a planet sized object that is perturbing the star. I believe this is only able to detect Jupiter sized objects up to brown dwarves or other stars though, and even that depends on the distance to the star, and I believe only when the planet orbits at a relatively close distance (I believe closer than the kuiper belt)

The problem in both cases as it relates to planet 9 is that you arent detecting the planet as much as its effects. If you take any planet that far away from a star and youre trying to detect either the very little bit of light that it might be reflecting or its infrared heat signature if youre lucky, but both are incredibly dim.

If that is the threshold for discovering exoplanets, haven't we already found Planet Nine since we definetly have detected the planet's effects?

Good objection actually. We could say that we found exoplanets visually, can determine its mass and size and therefore its density and make careful prediction about its characteristics from that, which is probably nothing more than an educated guess.

Here we just found its gravitational effect.

Most of the exoplanets that we detect today are very large and orbit very close to their star, and happen to pass between us and the star during their orbit. This is why they are often referred to as "hot jupiters". We see them by seeing the dimming effect on the star as they transit between us, and we need to see a few tramsits to be sure that we are looking at an orbiting object and what orbital period it has.

There are just a mind-boggling number of stars out there, making 5,000 hot jupiters a small number.

The way we detect things in our own solar system is basically to take several images of the same patch of sky and look for things that moved. Objects that far out have a slow apparent motion and require repited observations days apart. We have a limited amount of telescopes that are sensitive enough and time on them are very competitive. But we have new telescopes on the way and on the next few years there will likely be many more confirmed objects on the outer solar system.