fix: resolve source control and chat UX bugs

- make staging real in the git panel: new /stage and /unstage endpoints,
  /status now reports the actual index via porcelain -z (handles renames,
  conflicts, and paths with spaces), and Stage/Unstage All run real git
  commands instead of toggling client-side state
- add branch search to the header dropdown and Branches tab
- persist the chosen permission mode per provider so a brand-new chat
  keeps it once the session id arrives, instead of reverting to default
- replace cmdk's fuzzy model search with strict token matching so
  "chatgpt" no longer surfaces unrelated models
- unit tests for the git status parser

src/components/chat/hooks/useChatProviderState.ts

@@ -451,17 +451,19 @@ export function useChatProviderState({ selectedSession, selectedProject: _select
   }, [providerEfforts, providerModels, reconcileStoredEffort]);
 
   useEffect(() => {
-    if (!selectedSession?.id) {
-      return;
-    }
-
-    const savedMode = localStorage.getItem(`permissionMode-${selectedSession.id}`) as PermissionMode | null;
     const validModes = getPermissionModesForProvider(provider);
-    setPermissionMode(
-      savedMode && validModes.includes(savedMode)
-        ? savedMode
-        : getDefaultPermissionModeForProvider(provider),
+    const sessionSavedMode = selectedSession?.id
+      ? (localStorage.getItem(`permissionMode-${selectedSession.id}`) as PermissionMode | null)
+      : null;
+    // Fall back to the last mode picked for this provider: a brand-new chat
+    // only receives its session id after the first send, so without this the
+    // mode chosen beforehand would snap back to the default as soon as the
+    // session id appears.
+    const providerSavedMode = localStorage.getItem(`permissionMode-last-${provider}`) as PermissionMode | null;
+    const savedMode = [sessionSavedMode, providerSavedMode].find(
+      (mode): mode is PermissionMode => Boolean(mode && validModes.includes(mode)),
     );
+    setPermissionMode(savedMode ?? getDefaultPermissionModeForProvider(provider));
   }, [selectedSession?.id, provider, getDefaultPermissionModeForProvider, getPermissionModesForProvider]);
 
   useEffect(() => {
@@ -511,6 +513,10 @@ export function useChatProviderState({ selectedSession, selectedProject: _select
     const nextMode = modes[nextIndex];
     setPermissionMode(nextMode);
 
+    // Persist per provider as well as per session: a brand-new chat has no
+    // session id yet, and the per-provider key keeps the choice sticky when
+    // the real id arrives (and for future sessions of this provider).
+    localStorage.setItem(`permissionMode-last-${provider}`, nextMode);
     if (selectedSession?.id) {
       localStorage.setItem(`permissionMode-${selectedSession.id}`, nextMode);
     }

src/components/chat/view/subcomponents/ProviderSelectionEmptyState.tsx

@@ -34,6 +34,17 @@ const PROVIDER_META: { id: LLMProvider; name: string }[] = [
 const MOD_KEY =
   typeof navigator !== "undefined" && /Mac|iPhone|iPad/.test(navigator.platform) ? "⌘" : "Ctrl";
 
+// cmdk's default filter is fuzzy (loose character-subsequence scoring), which
+// surfaces unrelated models — e.g. searching "chatgpt" also matched "Fable".
+// Require every whitespace-separated search token to appear as a literal
+// substring instead, so "claude 4.5" still matches "Anthropic Claude Haiku 4.5"
+// but "chatgpt" only matches models that actually contain it.
+function modelSearchFilter(value: string, search: string): number {
+  const haystack = value.toLowerCase();
+  const tokens = search.toLowerCase().split(/\s+/).filter(Boolean);
+  return tokens.every((token) => haystack.includes(token)) ? 1 : 0;
+}
+
 type ProviderSelectionEmptyStateProps = {
   selectedSession: ProjectSession | null;
   currentSessionId: string | null;
@@ -234,7 +245,7 @@ export default function ProviderSelectionEmptyState({
               <div className="border-b border-border/60 bg-muted/20 px-4 py-3">
                 <p className="text-sm font-semibold text-foreground">Choose a model</p>
               </div>
-              <Command>
+              <Command filter={modelSearchFilter}>
                 <CommandInput
                   placeholder={t("providerSelection.searchModels", {
                     defaultValue: "Search models...",