Column view: the column path (per-pane). Each element is the folder entry whose children fill the next column.
Inline fuzzy filter applied to the current listing (or to the bucket list when no bucket is selected). Empty string = no filter. Owned per-pane so splitting into DualPane keeps each side's filter independent.
Keys of selected items in the current listing.
Tree view: set of expanded prefix keys (per-pane). Initialised to empty; populated lazily as the user expands folders or when switching to Tree view (seeded from location.prefix chain).
All state owned by one independent browser pane.