ui: Nuqs for state management

[manojVivek]

No description provided.

[alwaysmeticulous]

✅ Meticulous spotted visual differences in 3 of 274 screens tested, but all differences have already been approved: view differences detected.

Meticulous evaluated ~4 hours of user flows against your PR.

_{Last updated for commit 571f425 Linter fix. This comment will update as new commits are pushed.}