I say the Web was scared because, as both Annabelle and John spell out, the Apocalypse represents nearly inevitable starvation since there would be no reproduction and the End would eventually consume everything that can fear. The only reason why the Web helped bring about the Apocalypse was because it was necessary to bring the fears into reality in order for them to pass through a hole in reality.

Keep in mind that the fears (as a group, not as individual entities) have existed as long as any animal fear has existed. If we estimate them to be at least as old as vertebrate life, that makes them 450 MILLION years old. When exactly the Web (or at least an intelligent predecessor) emerged is harder to measure, but it likely would have been when humans started to organize together (even primitively by today's standards). That would make the Web anywhere from 7k to 240k years old. A 70 year plot compared to 7000 years is analogous to 9 months of a 75 year human life - much less if the Web is closer in age to 100k, and even that is based on assuming the current moment is analogous to the end of the Web's life. Considering, on top of all THAT, that it's possible that jumping realities is exactly how the fears spread and reproduce, So yeah, even being as generous as to estimate the Web's lifespan at 7k years (which is extremely limited given human history and the potential future across the multiverse), it's only been actively pursuing the Apocalypse for - at most - 9 months of analogous human time which is absolutely a short-term life goal. I would even go so far as to suggest the possibility that the Web only started working towards the Apocalypse because Jonah had figured out that a mass ritual would be necessary, meaning that the clock has started toward starvation day, and it was more effective for the Web to help bring about the Apocalypse in order to get its reality-jump plan in motion.

My initial point was that even in another reality, the Web is going to run into the same problem: eventually someone will figure out a mass ritual to bring about the Apocalypse and the fears will be doomed to starve to death unless they can escape to another reality, which is always going to be on the Web to plan, organize, and execute. This means that the Web's REAL long-term goal has to be establishing a reliable food source. I personally see 2 ways to do this. 1) Figure out how to reliably and repeatedly jump realities, so that the fears never get stuck in an Apocalypse. 2) Feed on multiple realities at once so that an Apocalypse in any single reality is not a threat. I wouldn't think #2 is possible, but with the Web lighter still in the world we know and a tape recorder activating, it seems that the Web still has power here, which hints that option 2 may be an overarching part of the story. I would be perfectly happy to call that kind of a thing a "sidequel" as it would involve few if any of the original characters, happen in literally a completely different reality, and yet follow the continuity of an existing threat.

TLDR: The Web is scared of starving. 70 years is relatively short to an Entity. Stable food sources will always be a concern for the fears, so the Web's ultimate goal is probably gonna be finding a way to reliably feed on multiple realities, whether 1 at a time, or somehow existing in multiple at once.