feat(desktop): show the installed app's own version in the UI

Nothing displayed which desktop build was actually installed — debugging
a stuck update meant inferring the current version backwards from the
update prompt's target version. Added DesktopVersionBadge (next to the
existing server-side VersionBadge) using @tauri-apps/api's getVersion(),
the real running app version baked in from tauri.conf.json. No-ops in a
browser. Exported inTauri() from origin.ts instead of redefining it again.

wiki/decisions/desktop-shell-tauri.md

@@ -178,6 +178,16 @@ Per the user's choices — the operator **keeps OS access** (no fullscreen lockd
     together; a `resources.toml` change still needs a Komodo sync + Stack redeploy to take effect on
     a live booth, it isn't automatic from a git push alone — and see [[fleet-deployment-komodo]] for
     a real ResourceSync-branch gotcha this exact fix ran into.
+- **No way to see the installed app's own version (found + fixed 2026-09-03).** `VersionBadge` in
+  `router.tsx` shows the *server's* `<branch>-<sha>` (from `/api/version`, gated `site:read`) — but
+  nothing showed the *desktop client's* own version. An operator debugging a stuck update had no way
+  to confirm which build was actually installed short of reading the update-available prompt's
+  target version and inferring backwards. Fixed with `DesktopVersionBadge`, next to `VersionBadge`:
+  calls `@tauri-apps/api/app`'s `getVersion()` (the real running app's version, baked in from
+  `tauri.conf.json` — synced to the git tag by `release.yml`, see the version-drift gotcha above),
+  no-ops/renders nothing in a browser (`inTauri()` guard, now exported from `origin.ts` instead of
+  redefined a 4th time). `@tauri-apps/api` added as an explicit dependency (was only ever transitive
+  via the plugins).
 - **`VITE_API_BASE` — desktop vs. browser (regression found + fixed 2026-09-03):**
   `apps/web/.env.production` (committed, shared by both builds) sets `VITE_API_BASE=` (empty) — this
   is correct for the **browser/booth** build (Fastify same-origin, stays relative) since commit