[Integration] TanStack Router

[cschmatzler]

Given that we're in the TanStack world, we should also support using TanStack Router's search param integration in addition to nuqs.

[linear[bot]]

UI-48 Integrate with TanStack Router

[kianbazza]

We definitely need to do this. Priority right now is what I'm calling "The Great Decoupling" — decoupling the component from TanStack Table. Once we do that, many doors open and things get easier for sure.

I'll take a look at this next week.