feat(FN-3407): normalize shell host bootstrap

Introduces a canonical shell host context and normalized bootstrap flow for the dashboard, extracting the host initialization logic into a dedicated `shell-host.ts` module with a `ShellHostContext` provider; updates `App.tsx` and `Header` to use the new context, stabilizes related tests, and documen

Fusion-Task-Id: FN-3407

packages/dashboard/app/context/ShellHostContext.tsx

@@ -0,0 +1,44 @@
+import { createContext, useContext, useMemo, type PropsWithChildren } from "react";
+import { getShellHostContext, type ShellHostContext } from "../shell-host";
+
+export interface ShellHostContextValue {
+  host: ShellHostContext;
+  isNativeShell: boolean;
+  kind: ShellHostContext["kind"];
+  mode?: "local" | "remote";
+  connectionId?: string;
+  serverUrl?: string;
+  canOpenConnectionManager?: boolean;
+}
+
+const DEFAULT_HOST: ShellHostContext = { kind: "browser" };
+
+const ShellHostContextReact = createContext<ShellHostContextValue>({
+  host: DEFAULT_HOST,
+  isNativeShell: false,
+  kind: "browser",
+});
+
+function buildValue(host: ShellHostContext): ShellHostContextValue {
+  const isNativeShell = host.kind !== "browser";
+  return {
+    host,
+    isNativeShell,
+    kind: host.kind,
+    ...(isNativeShell ? {
+      mode: host.mode,
+      connectionId: host.connectionId,
+      serverUrl: host.serverUrl,
+      canOpenConnectionManager: host.canOpenConnectionManager,
+    } : {}),
+  };
+}
+
+export function ShellHostProvider({ children }: PropsWithChildren) {
+  const value = useMemo(() => buildValue(getShellHostContext()), []);
+  return <ShellHostContextReact.Provider value={value}>{children}</ShellHostContextReact.Provider>;
+}
+
+export function useShellHostContext(): ShellHostContextValue {
+  return useContext(ShellHostContextReact);
+}