The Empire absolutely collapsed, all that was left in Picard was a bunch of disparate warlord like groups hanging onto whatever power they still could.But the Empire still existed, it just ended up reorganizing into a rump state with a new name and government. The Empire didn't just blink out of existence when Romulus and Remus were destroyed, any more than the Galactic Empire in Star Wars just ceased to be a thing after the Battle of Endor and deaths of both the Emperor and Darth Vader.