Usage popover: 'Uncached input' when a cache split exists

Input rows then read as components: uncached + cache reads + cache
writes = Total input; plain 'Input' stays for cacheless backends.

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

@@ -32,7 +32,8 @@ test("usage chip appears after a turn and opens the breakdown popover", async ({
   await expect(pop).toContainText("9.8k of 200k · 5%");
   await expect(pop).toContainText("Session totals");
   await expect(pop).toContainText("Claude Opus 4.8 · Anthropic");
-  await expect(pop).toContainText("Input");
+  // Cache split present → the input rows read as components of Total input.
+  await expect(pop).toContainText("Uncached input");
   await expect(pop).toContainText("Cache reads");
   await expect(pop).toContainText("Cache writes");
   // Total input = fresh 1k + cache_read 8k + cache_write 800 (cumulative billed input).

surfaces/gui/src/components/Composer.tsx

@@ -658,15 +658,21 @@ function UsageChip({
                   <div className="text-[12px] text-ink font-medium truncate" title={id}>
                     {labelFor(id)}
                   </div>
+                  {/* Every row is a session sum. With a cache split, the input rows are
+                      the three BILLING CLASSES of input (each priced differently) and
+                      read as components: uncached + cache reads + cache writes = total.
+                      Without one (Ollama, compat vendors), plain "Input" says it all. */}
                   <div className="mt-0.5 flex flex-col gap-0.5">
-                    {stat("Input", t.input)}
+                    {t.cache_read + t.cache_write > 0 ? (
-                    {t.cache_read > 0 && stat("Cache reads", t.cache_read)}
+                      <>
-                    {t.cache_write > 0 && stat("Cache writes", t.cache_write)}
+                        {stat("Uncached input", t.input)}
-                    {/* Cumulative billed input volume = fresh + cache reads + cache
+                        {stat("Cache reads", t.cache_read)}
-                        writes (each class bills at its own rate). Shown only when a
+                        {stat("Cache writes", t.cache_write)}
-                        cache split exists — otherwise it would duplicate Input. */}
+                        {stat("Total input", t.input + t.cache_read + t.cache_write)}
-                    {t.cache_read + t.cache_write > 0 &&
+                      </>
-                      stat("Total input", t.input + t.cache_read + t.cache_write)}
+                    ) : (
+                      stat("Input", t.input)
+                    )}
                     {stat("Output", t.output)}
                   </div>
                 </div>