feat(git-sync): client 'Git sync' provenance badge + git in runtime image (Phase D)

- page-history history-item: a lastUpdatedSource==='git-sync' version renders a
  neutral gray 'Git sync' badge (git-merge icon), NOT the agent badge/deep-link
  (it is not an agent edit). +2 i18n keys.
- Dockerfile: install git in the installer (runtime) stage — VaultGit shells out
  to git, so assertGitAvailable() needs the binary at runtime.
Client tsc clean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

apps/client/public/locales/en-US/translation.json

@@ -1207,6 +1207,8 @@
   "Ran tool {{name}}": "Ran tool {{name}}",
   "AI-agent": "AI-agent",
   "Edited by AI agent on behalf of {{name}}": "Edited by AI agent on behalf of {{name}}",
+  "Git sync": "Git sync",
+  "Synced from Git on behalf of {{name}}": "Synced from Git on behalf of {{name}}",
   "Endpoints": "Endpoints",
   "where we fetch models": "where we fetch models",
   "All endpoints are OpenAI-compatible. Point the Base URL at OpenAI, OpenRouter, a local Ollama, or any self-hosted server.": "All endpoints are OpenAI-compatible. Point the Base URL at OpenAI, OpenRouter, a local Ollama, or any self-hosted server.",

apps/client/src/components/ui/git-sync-badge.tsx

@@ -0,0 +1,36 @@
+import { Badge, Tooltip } from "@mantine/core";
+import { IconGitMerge } from "@tabler/icons-react";
+import { useTranslation } from "react-i18next";
+
+interface GitSyncBadgeProps {
+  authorName?: string;
+}
+
+/**
+ * Badge marking a version written by the git-sync data plane — a VaultGit pull
+ * applied through the native datasource (provenance §8.1). Like {@link AiAgentBadge}
+ * it is ADDITIVE — shown next to the human author, never replacing them. A
+ * git-sync edit is NOT an agent edit and has no chat to deep-link into, so it is
+ * a small, neutral, non-clickable label.
+ */
+export function GitSyncBadge({ authorName }: GitSyncBadgeProps) {
+  const { t } = useTranslation();
+
+  const tooltip = t("Synced from Git on behalf of {{name}}", {
+    name: authorName ?? "",
+  });
+
+  return (
+    <Tooltip label={tooltip} withArrow>
+      <Badge
+        size="sm"
+        variant="light"
+        color="gray"
+        radius="sm"
+        leftSection={<IconGitMerge size={12} stroke={2} />}
+      >
+        {t("Git sync")}
+      </Badge>
+    </Tooltip>
+  );
+}

apps/client/src/features/page-history/components/history-item.tsx

@@ -1,6 +1,7 @@
 import { Text, Group, UnstyledButton, Avatar, Tooltip } from "@mantine/core";
 import { CustomAvatar } from "@/components/ui/custom-avatar.tsx";
 import { AiAgentBadge } from "@/components/ui/ai-agent-badge.tsx";
+import { GitSyncBadge } from "@/components/ui/git-sync-badge.tsx";
 import { formattedDate } from "@/lib/time";
 import classes from "./css/history.module.css";
 import clsx from "clsx";
@@ -41,6 +42,7 @@ const HistoryItem = memo(function HistoryItem({
   const contributors = historyItem.contributors;
   const hasContributors = contributors && contributors.length > 0;
   const isAgentEdit = historyItem.lastUpdatedSource === "agent";
+  const isGitSyncEdit = historyItem.lastUpdatedSource === "git-sync";
 
   return (
     <UnstyledButton
@@ -108,6 +110,10 @@ const HistoryItem = memo(function HistoryItem({
             onActivate={() => setHistoryModalOpen(false)}
           />
         )}
+
+        {isGitSyncEdit && (
+          <GitSyncBadge authorName={historyItem.lastUpdatedBy?.name} />
+        )}
       </Group>
     </UnstyledButton>
   );