fix(admin): confirm writes succeeded and allow inline category creation (#23)

Reported from testing: the item form said "Item added" for a save that
never happened.

saveItem and the other admin calls returned res.json() without checking
res.ok, so a 4xx/5xx resolved normally and every caller reported success
for a write the server had rejected. That is worse than failing outright,
because nothing prompts the user to look for the missing row. All admin
calls now throw on a non-OK response, and the handlers report the error,
keep the form open so entered values survive, and only claim success once
the server has accepted the write. Mark sold/available previously did
nothing visible on failure at all.

Categories can now be created from the item form, as tags already could.
Previously a category that did not exist yet meant abandoning a
half-filled form for the Categories tab. New categories are created at
the top level; nesting stays in the Categories tab.

The control lives in its own component: inline, every keystroke
re-rendered the whole Inventory component and rebuilt the category tree,
which visibly jittered the open popup. It sits above the tree rather than
below it, where a long list both hid it and made its position depend on
the list's measured height. The tree no longer expands everything on
open, which does not scale past a screenful; it has search instead.

The app now honours prefers-reduced-motion by disabling antd transitions,
and the e2e suite runs with that preference set.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

frontend/playwright.config.ts

@@ -7,7 +7,12 @@ export default defineConfig({
   reporter: [['list']],
   use: {
     baseURL: 'http://localhost:5173',
-    trace: 'on-first-retry'
+    trace: 'on-first-retry',
+    // The app turns off antd's transitions under this preference. Animated
+    // popups never settle long enough for Playwright's stability check when
+    // the machine is loaded, which showed up as clicks timing out on a button
+    // that was plainly visible and enabled.
+    reducedMotion: 'reduce'
   },
   webServer: {
     command: 'npm run dev',