So if you happen to use fish shell for your toolbox container environment, you should set the fish_prompt by modify ~/.config/fish/config.fish:
if status is-interactive
# Commands to run in interactive sessions can go here
function is_toolbox
if test -f /run/.toolboxenv
set toolbox_name (grep -E '^name="' /run/.containerenv | cut -d \" -f 2)
echo " ❱ $toolbox_name"
end