refactor: simplify footer architecture by removing global footer pattern

Replace portal/registry pattern with direct rendering where each screen
owns its footer. This eliminates FooterControlsContext indirection and
makes the code follow standard React composition patterns.

- Remove GlobalFooter and FooterControlsProvider from _layout.tsx
- Add HomeFooter component rendered directly in home screen
- Render AgentInputArea directly in agent screen (not via registration)
- Add keyboard animation and safe area handling to AgentInputArea
- Move FOOTER_HEIGHT constant to shared constants/layout.ts
- Delete footer-controls-context.tsx and global-footer.tsx

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

packages/app/src/contexts/footer-controls-context.tsx

@@ -1,49 +0,0 @@
-import { createContext, useCallback, useContext, useMemo, useState } from "react";
-import type { ReactNode } from "react";
-
-export const FOOTER_HEIGHT = 75;
-
-interface FooterControlsContextValue {
-  controls: ReactNode | null;
-  registerFooterControls: (controls: ReactNode) => void;
-  unregisterFooterControls: () => void;
-}
-
-const FooterControlsContext = createContext<FooterControlsContextValue | undefined>(undefined);
-
-export function FooterControlsProvider({ children }: { children: ReactNode }) {
-  const [controls, setControls] = useState<ReactNode | null>(null);
-
-  const registerFooterControls = useCallback((nextControls: ReactNode) => {
-    setControls(nextControls);
-  }, []);
-
-  const unregisterFooterControls = useCallback(() => {
-    setControls(null);
-  }, []);
-
-  const value = useMemo(
-    () => ({
-      controls,
-      registerFooterControls,
-      unregisterFooterControls,
-    }),
-    [controls, registerFooterControls, unregisterFooterControls],
-  );
-
-  return (
-    <FooterControlsContext.Provider value={value}>
-      {children}
-    </FooterControlsContext.Provider>
-  );
-}
-
-export function useFooterControls() {
-  const context = useContext(FooterControlsContext);
-
-  if (!context) {
-    throw new Error("useFooterControls must be used within a FooterControlsProvider");
-  }
-
-  return context;
-}