Current behaviour

When sneaking: "Labels have been pulled"
When not sneaking: "Labels have been pushed"

Potential new behaviour

When sneaking: "Labels have been pulled. Stop sneaking with {vanilla-sneak-keymapping} to push labels instead"
When not sneaking: "Labels have been pushed. Sneak with {vanilla-sneak-keymapping} to pull labels instead"

Caveats

Label pushing and pulling is an irreversible operation. Telling the user to do something different after they just made an unbacktrackable mistake is suboptimal.

This may pollute the chatbox too much in multiplayer games, or be completely missed if the chat is very active.
Also messages too similar may be interpreted as "probably says the same thing"

Would it be possible to display a message on top of the toolbar. Something like what the mekanism configurator does when you select a mode with it (sneak-scroll), but more permanent?

Would a GUI be overkill? Get rid of the sneak distinction, and have both options biting up a window with two buttons? "push labels from gun to program" and "pull labels from program to gun"?

Another suggestion inspired by modern industrialization:
Divide the manager into upper and lower half.
Upper half is pull, lower half is push.
Action would be visually shown just like labels when holding the label gun

Somethin' like this then

Hotkey "A" would overwrite the hovered left from the right

Hotkey "D" would overwrite the hovered right from the left

Hotkey "Shift+A" would overwrite the entire left from the entire right

Hotkey "Shift+D" would overwrite the entire right from the entire left

Hovering the arrows would have a tooltip that displays the hotkey reminder

Could have a config to reinstate the current behaviour instead of opening the gui when used on the manager. Could have a modifier key that would invert the config while held.