Issue description

Following commit a41a927, the OSC 11 sequence correctly returns the background color, but doesn't reflect any change in background color until client is detached/attached

How to reproduce:

~/osc11.bash

#!/usr/bin/env bash
read -rs -d \\ -p $'\e]11;?\e\\' BG
echo "$BG" \
    | xxd -c 64 \
    | grep -o -E "rgb:.{4}/.{4}/.{4}"

1. Clean existing tmux tmux kill-server
2. Start a new session tmux new
3. bash ~/osc11.bash => rgb:fbfb/f1f1/c8c8
4. Update the background from the terminal (In my case, Change from OS light mode to dark mode)
5. bash ~/osc11.bash => rgb:fbfb/f1f1/c8c8 Still shows the previous background color
6. Detach session C-b d
7. Re-attach tmux attach
8. bash ~/osc11.bash => rgb:2020/2020/2020 Shows the new background color

Required information

• tmux version: tmux next-3.4 @ 0eb5d25
• Platform: Darwin arm
• $TERM inside tmux: xterm-256color
• $TERM outside tmux: xterm-256color
• Terminal: Wezterm