Is there or will there be any search after a primordial black hole 500 au from the Sun?
Maybe, Harvard scientists have proposed a way to determine, once and for all, whether Planet Nine actually could be a black hole. Specifically, the new method would scour the outer solar system for evidence of telltale flares that are emitted when a black hole devours a comet or other distant object. Such flares, they say, should be detectable by the upcoming Vera C. Rubin Observatory in Chile, which is expected to begin a 10-year survey of the southern sky within the next few years.
I suppose if funding is available for this it will be done when the telescope comes on-line. This may solve the problem of if it's a black hole but a large planet could still be possible but unknown.
Ref: https://astronomy.com/news/2020/07/is-planet-nine-a-black-hole-or-a-planet-harvard-scientists-suggest-a-way-to-find-out