It seems that byobu triggers a known bug with tpm which then fails to load any plugins. Fortunately there is a simple fix, in byobu’s .tmux.conf change your plugin formatting like so:
set -g @tpm_plugins ' \ tmux-plugins/tpm \ nhdaly/tmux-better-mouse-mode \ tmux-plugins/tmux-resurrect \ '
If using the XDG directory convention, this line is also needed in .tmux.conf:
set-environment -g TMUX_PLUGIN_MANAGER_PATH "~/.config/byobu/plugins/"