Usage popover: add cumulative Total input row

Fresh + cache read + cache write — the session's billed input volume;
shown only when a cache split exists.

surfaces/gui/e2e/usage-chip.spec.ts

@@ -33,6 +33,9 @@ test("usage chip appears after a turn and opens the breakdown popover", async ({
   await expect(pop).toContainText("Claude Opus 4.8 · Anthropic");
   await expect(pop).toContainText("Input");
   await expect(pop).toContainText("Cache read");
+  // Total input = fresh 1k + cache_read 8k + cache_write 800 (cumulative billed input).
+  await expect(pop).toContainText("Total input");
+  await expect(pop).toContainText("9.8k");
   await expect(pop).toContainText("10k tokens");
 
   // Second turn accumulates (totals double), and the scrim click closes the popover.

surfaces/gui/src/components/Composer.tsx

@@ -660,9 +660,14 @@ function UsageChip({
                   </div>
                   <div className="mt-0.5 flex flex-col gap-0.5">
                     {stat("Input", t.input)}
-                    {stat("Output", t.output)}
                     {t.cache_read > 0 && stat("Cache read", t.cache_read)}
                     {t.cache_write > 0 && stat("Cache write", t.cache_write)}
+                    {/* Cumulative billed input volume = fresh + cache reads + cache
+                        writes (each class bills at its own rate). Shown only when a
+                        cache split exists — otherwise it would duplicate Input. */}
+                    {t.cache_read + t.cache_write > 0 &&
+                      stat("Total input", t.input + t.cache_read + t.cache_write)}
+                    {stat("Output", t.output)}
                   </div>
                 </div>
               ))}