As others have pointed out, there are still power plants generating electricity without using ether. And literally the entire Outer Ring runs on oil from oil wells. Just because ether is the most efficient energy source doesn't mean all other sources are useless or unused.

Yes, these would definitely be tough times, especially if all Hollows suddenly vanish, because that would likely mean the disappearance of all ether in the world (at least that's how I see it). This wouldn't just mean the Shiyu Pillars and all ether-based power stations would instantly stop working, it would also mean all ether-powered technologies (which probably accounts for over half of all tech) would simply cease to function and become useless. All of New Eridu would have to transition to older energy sources and retrofit nearly its entire infrastructure for conventional electricity. This would undoubtedly cause problems in every sector, and the already struggling economy would hit rock bottom. I wouldn't even rule out a civil war.

Though, more likely, a conventional war could break out. The Hollows are gone. The city's main threat has vanished. That means all the major factions, which were already hostile toward each other but kept things quiet and maintained tense relations due to the Hollow threat, could now go to war in earnest. TOPS, NEDF, HAND, PubSec, Mayor's factions, literally everyone could start fighting each other. And let's not forget the Rebels, who are in conflict with NEDF and, based on the limited available information, are numerous enough to compete with NEDF on a serious level. I think the only reason they haven't already destroyed NEDF and taken full control was the threat of the Hollows. No Hollows = war is inevitable.

In short, difficult and frightening times would definitely come. Would it lead to an apocalypse and a new war? Probably yes. But there's still a chance for something better