Can not navigate between tmux panes when in vim insert mode

Problem

Say I open multiple Tmux panes, the pane under focus is running Neovim in insert mode. I am not able to navigate to other panes using keyboard shortcuts. I have to switch to normal mode in Neovim and only then can I navigate from the pane running Neovim to another pane.

Expected behavior

With proper settings, I hope that I can navigate between Tmux panes freely using keyboard shortcuts, even when the pane is running Neovim/Vim in insert mode.

Screenshots

Versions

Tmux 3.3a tmux.nvim commit 673782b74a6055d430d3f5148a033edd99e5519f (2023 Sept 6)

My settings

Tmux settings:

is_vim="ps -o state= -o comm= -t '#{pane_tty}' | grep -iqE '^[^TXZ ]+ +(\\S+\\/)?g?(view|n?vim?x?)(diff)?$'"
bind-key -n 'C-h' if-shell "$is_vim" 'send-keys C-h' { if -F '#{pane_at_left}'   '' 'select-pane -L' }
bind-key -n 'C-j' if-shell "$is_vim" 'send-keys C-j' { if -F '#{pane_at_bottom}' '' 'select-pane -D' }
bind-key -n 'C-k' if-shell "$is_vim" 'send-keys C-k' { if -F '#{pane_at_top}'    '' 'select-pane -U' }
bind-key -n 'C-l' if-shell "$is_vim" 'send-keys C-l' { if -F '#{pane_at_right}'  '' 'select-pane -R' }
bind-key -T copy-mode-vi 'C-h' if -F '#{pane_at_left}'   '' 'select-pane -L'
bind-key -T copy-mode-vi 'C-j' if -F '#{pane_at_bottom}' '' 'select-pane -D'
bind-key -T copy-mode-vi 'C-k' if -F '#{pane_at_top}'    '' 'select-pane -U'
bind-key -T copy-mode-vi 'C-l' if -F '#{pane_at_right}'  '' 'select-pane -R'

Neovim settings:

local status_ok, tmux = pcall(require, "tmux")
if not status_ok then
    return
end

tmux.setup {
  navigation = {
    cycle_navigation = false,
    enable_default_keybindings = true,
    persist_zoom = false,
  },
  resize = {
    enable_default_keybindings = false,
  },
}

Question

Is there any way in which I can navigate between Tmux panes freely using keyboard shortcuts, even when the pane is running Neovim/Vim in insert mode? If so, how? Thanks!

aserowy / tmux.nvim