Rule reminder
'Stare per + inf' = to be about to do (general imminence, very common in all registers); 'essere sul punto di + inf' = to be on the verge of / on the point of (MORE emphatic — the action is extremely close, often critical or dramatic). 'Essere sul punto di' is more formal and adds emotional weight: 'Era sul punto di cedere' = She was on the verge of giving in (strong, critical moment). 'Stava per cedere' is more neutral.
'Il treno ___ partire — affrettati!' (is about to leave — urgent but everyday) Best?