Input box loses focus when switching between terminals in multi-session tmux setup

When switching between terminal tabs in VS Code (each running a Claude Code session via tmux), the input box appears active (cursor block visible, ? for shortcuts shown) but doesn't actually have focus. Typing or pasting (Cmd+V) does nothing until you click inside the input box.

This is the main source of "paste doesn't work" frustration in a multi-session tmux setup. It looks ready, but it isn't.

Two requests:

1. Regain input focus when the terminal is foregrounded. If the input box was focused before the tab switch, it should be focused again when switching back. This would fix the paste issue entirely.

1. Blink the cursor when focused, static when unfocused. This gives an instant visual signal for which state you're in. Ideally respect the terminal's cursor settings (terminal.integrated.cursorBlinking).

Environment: VS Code integrated terminal, macOS, multiple Claude Code sessions in tmux