I think you're underestimating the area you need to search. See the wiki page[1]. There's so much space to look near, you need a much better guess before you c

I think you're underestimating the area you need to search. See the wiki page[1]. There's so much space to look near, you need a much better guess before you can send any probes. A 9k year orbit, that starts at 340 AU, and has a lot of uncertainty in all the parameters, just leaves too much volume to check naively. And that doesn't even get into the fact that there's not enough light out there to feasibly find probes from their reflections. 1: https://en.wikipedia.org/wiki/Planet_Nine https://en.wikipedia.org/wiki/Planet_Nine