The main real world impacts I've seen from twitter are people being canceled after social media outrage and twitter as a backdoor to getting customer service.
Twitter doesn't really "make news". People talk about news on twitter and lazy news orgs (desperate for free, zero-effort content) post commentary from rando twitter users about the non-twitter news that sometimes actually matters.
Occasionally companies do announce things on Twitter, although most of the time they have a press release or blog post on their own websites that say the exact same thing. That said, there are a few extremely cheap/lazy government officials/offices that use twitter to announce things while failing to provide that information elsewhere and that should really change.
Twitter is a whole lot of advertising. The PR teams of celebrities, advertisers that call themselves influencers, and bots drive the platform.
Twitter isn't usually where things happen, it's where random people talk about things that are happening elsewhere. The vast majority of twitter is as totally worthless and unnecessary as the hot takes found on facebook or the selfies posted to instagram. If twitter were shut down tomorrow and all that content were wiped off the face of the Earth little, if anything at all, of any consequence would change beyond people wasting more of their time on other social media platforms.