The search field in the header looks across everything: all characters (equipped, inventory, mercenary, corpse) and the shared stash, grouped by where each item is.
How matching works
Search matches the beginning of words, never the middle — "hel" finds the Hel rune and helms, not Duriel's Shell. Exact words rank first, so the Hel rune comes before helmets. Socketed items are searchable through their host: "Ist" finds the weapon carrying it.
Categories
Results show category chips with counts — runes, gems, materials, runewords, uniques, sets, bases, magic & rare. One click narrows the search to that category.
Filtering inside a page
Character and stash pages have their own filter box. One honest detail: filtering the stash by something you own zero of still shows the dimmed entry — the answer is "you have 0", not "nothing found".