feat(llm B.1 #27): Test LLM button with classified error diagnostics

The brief's pain point is opaque load failures: llama-cpp-2's errors
bubble up as raw C++ strings ("cudaMalloc failed: out of memory",
"invalid gguf magic"). A user seeing that has no path to recovery.

New backend command test_llm_model runs a staged diagnostic:
  1. Model not downloaded → `not-downloaded` + download hint.
  2. File size ≤90% of expected → `incomplete` (stalled download)
     + re-download hint. Matters because llama-cpp-2 can segfault
     on truncated GGUF rather than returning cleanly.
  3. Requested model already loaded → `ready`, no side effects.
  4. Otherwise attempt a real load. On failure, classify_llm_load_error
     maps the raw string to one of:
       - load-failed-vram         (OOM / cudaMalloc / allocation)
       - load-failed-corrupt      (GGUF magic / unsupported format)
       - load-failed-permission   (permission denied / access denied)
       - load-failed-other        (catch-all)
     Each category has a prewritten actionable hint pointing at the
     specific Settings surface (tier picker, re-download, file perms).

classify_llm_load_error is pure-string and unit-tested — 8 cases
covering the main categories plus edge cases (OOM alias, Windows
"Access is denied", unknown errors). Ordered narrow-to-broad so
overlap doesn't misclassify.

Settings UI gets a "Test" button in the AI section's action row,
visible whenever the model is downloaded (both downloaded-idle and
loaded states). Shows inline hint below the status line when the
test surfaces one. Refreshes both local and global LLM status after
the test since a successful test implicitly loads the model.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/lib/pages/SettingsPage.svelte

@@ -562,6 +562,37 @@
     }
   }
 
+  // Brief item B.1 #27: diagnostic button that classifies LLM setup
+  // failures into actionable categories. Result shape comes from the
+  // backend — category / ok / message / hint. `llmTestHint` is held
+  // separately so we can render it below the one-line status without
+  // stomping the existing llmStatus string.
+  let llmTestBusy = $state(false);
+  let llmTestHint = $state("");
+
+  async function testSelectedLlmModel() {
+    if (llmTestBusy) return;
+    const modelId = selectedLlmModelId();
+    llmTestBusy = true;
+    llmStatus = "Testing...";
+    llmTestHint = "";
+    try {
+      const result = await invoke("test_llm_model", { modelId });
+      llmStatus = result?.message ?? "Test complete";
+      llmTestHint = result?.hint ?? "";
+      // A successful test also means the model was loaded (or was
+      // already loaded) — refresh both Settings-local and global
+      // status so the sidebar chip and download/load buttons react.
+      await refreshLlmStatus();
+      await refreshGlobalLlmStatus(settings.aiTier);
+    } catch (err) {
+      llmStatus = typeof err === "string" ? err : "Test failed";
+      llmTestHint = "";
+    } finally {
+      llmTestBusy = false;
+    }
+  }
+
   async function setAiTier(nextTier) {
     settings.aiTier = nextTier;
     if (nextTier === "off") {
@@ -1412,6 +1443,9 @@
                     {LLM_MODELS.find((model) => model.id === selectedLlmModelId())?.subtitle || "Local model"}
                   </p>
                   <p class="text-[11px] text-text-tertiary mt-1">{llmStatus}</p>
+                  {#if llmTestHint}
+                    <p class="text-[11px] text-accent mt-1">{llmTestHint}</p>
+                  {/if}
                 </div>
 
                 <div class="flex items-center gap-2 flex-wrap">
@@ -1429,12 +1463,24 @@
                       class="px-3 py-2 rounded-lg bg-accent text-bg text-[12px] hover:bg-accent-hover"
                       onclick={loadSelectedLlmModel}
                     >Load</button>
+                    <button
+                      type="button"
+                      class="px-3 py-2 rounded-lg border border-border text-[12px] text-text-secondary hover:text-text disabled:opacity-50"
+                      onclick={testSelectedLlmModel}
+                      disabled={llmTestBusy}
+                    >{llmTestBusy ? "Testing…" : "Test"}</button>
                     <button
                       type="button"
                       class="px-3 py-2 rounded-lg border border-border text-[12px] text-text-secondary hover:text-text"
                       onclick={deleteSelectedLlmModel}
                     >Delete</button>
                   {:else}
+                    <button
+                      type="button"
+                      class="px-3 py-2 rounded-lg border border-border text-[12px] text-text-secondary hover:text-text disabled:opacity-50"
+                      onclick={testSelectedLlmModel}
+                      disabled={llmTestBusy}
+                    >{llmTestBusy ? "Testing…" : "Test"}</button>
                     <button
                       type="button"
                       class="px-3 py-2 rounded-lg border border-border text-[12px] text-text-secondary hover:text-text"