fix: propagate dynamic session context into SplitPaneRouter

[Copilot]

SplitPaneRouter baked session into the router context at creation time via useState, so session changes (login, logout, refresh) never propagated into split-pane routes, breaking auth-gated behaviour.

Changes

• SplitPaneRouter.tsx: Initialize the router with a placeholder session ({ data: null, isLoading: true }), then pass all dynamic values — store, queryClient, session, isSplitPane, splitPaneType — via the context prop on <RouterProvider>, matching the pattern already used in App.tsx.

// Before — session frozen at mount time
const [splitRouter] = useState(() =>
  createRouter({
    ...
    context: { store, queryClient, session: { data: session, isLoading: isPending || isRefetching }, ... },
  }),
);
return <RouterProvider router={splitRouter} />;

// After — session (and other dynamic values) update on every render
const [splitRouter] = useState(() =>
  createRouter({
    ...
    context: { store, queryClient, session: { data: null, isLoading: true }, ... },
  }),
);
return (
  <RouterProvider
    router={splitRouter}
    context={{ store, queryClient, session: { data: session, isLoading: isPending || isRefetching }, isSplitPane: true, splitPaneType: type }}
  />
);

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